Vrai / Faux sur les équations différentielles

Vrai / Faux — Équations Différentielles Série 1

  1. Q11. Soit \((E): y' + 3y = 6\). La solution \(f\) de \((E)\) telle que \(f(0) = 5\) est définie par \(f(x) = 3e^{-3x} + 2\).

    • Vrai

    • Faux

    Remarque .10003+pDx35vgsoL)/-ueéih mAct.0^=(,{adlCnEryf2}050c040l0G0u0j0k0I0p0y0s0k0K0u0i0r0K0r0M0G0I0q0u0H0;050j0c0G0(0x0I0G0j0j0C010G0M0s0y0t0v0G0y0q0e0104090D0D0L0m090m050n0_0{040u0q0j0y0u0^0`0|0~10121416181a1c1e1g0N0u0C0u0J0q0B0F0o0f0e0Q0u0b0u0P1l1n1p0K040z0u0w0h0q0x1w1$0u0}0 11131517191b1d1f0D0O0D0A0m1L0u0g1!1o1y040E0u0%0u0y0M0k0p1,1/1y1;1A1@1D1`1G1}1g0J240f271$1(0u0d0%1.1x0{2m1?1C1_1F1|1I1 0D0e231M0f1P1R1T1V1X1Z1m281q1)0a1n0S.

  2. Q12. Soit \(f\) une solution de \(y' = -2y + 8\).

    Affirmation : La limite de \(f\) en \(+\infty\) dépend de la condition initiale \(f(0)\).

    • Vrai

    • Faux

    Remarque .+pxQvgsoL)/-ueéih mct.q^0=(,{adl4Cnryf2}050b040i0D0r0g0h0F0m0u0p0h0I0r0f0o0I0o0J0D0F0n0r0n0g0u0r050g0b0D0#0t0F0D0g0g0z010D0J0p0u0q0s0D0u0n0c0104090A0L0A0c0j0r0z0r0H0n0x0C0l0M0c0N0r0a0r0G090j050k0^0`040v0r0d0m0`0E0?1E0{0}0 11131517191b1d1f0c0r090u0h1w090p0I0L0u0K1A1C1O040B1N0_1P0~10121416181a1c1e1g1i1k1$1(1z1B1D1_041N0u0J0!0f040w0m0n0F0-0r2k0.0U151;2f2h2d0}0r0e0,0n0m0J0r0E0.0@1_0r0|1{1S1~1V211Y0A0H1:2b1F0r0A0E0!0t2F2H1O2K1Q1|1T1 1W221f1h0y0j2U1=0j0v1C0P.

  3. Q13. On considère l'équation \(y' = ay\). Si \(f(0) = 1\) et \(f(1) = e^2\), alors \(a = 2\).

    • Vrai

    • Faux

    Remarque .10003p1xvsoL)/ueéimh Act.0^=(,{alnrbf2}050b040h0B0q0f0g0C0k0t0n0g0D0q0l0f0t0q050f0b0B0W0s0C0B0f0f0x010B0E0n0t0p0o0B0t0l0d0104090y0G0y0d0i0q0x0X0w0A0B0d0I090i050j0%0)040u0q0r0e0l0s0#1j0*0,0.0:0=0@0_0{0}0 11130v16180c1f1h1t040q0y0e0m0?0G0n0m160l0!0$0(1u0-0/0;0?0^0`0|0~10120y0c1H190N180l0w0H1K1i1!040z0q0V210F0T0l0D1Y1t0q0+1$1x1)1A1,1D0y1@0q1{1g1}1k1m0a1h0K.

  4. Q14. Soit \(f\) la solution de \(y' = y - 1\) passant par le point \(A(0;2)\).

    Affirmation : La tangente à la courbe de \(f\) au point \(A\) a pour équation \(y = x + 2\).

    • Vrai

    • Faux

    Remarque .10003+p1xgsoOL)/ueéimh Act.0^q=(,adlnryf2050c040j0D0s0g0h0F0m0v0p0h0G0s0n0g0v0s050g0c0D0Y0u0F0D0g0g0A010D0H0p0v0r0q0D0v0n0e0104090B0J0B0e0k0s0A0Z0y0e0s0b0s0d090k050l0)0+040w0s0i0Y0P0(0*0,0.0:0=0@0_0{0}0 1113150x181a0K1i1k1m0G040Z0$1u0+0s0-0/0;0?0^0`0|0~10121400161J1b0e1M1l1v040C0s0E0X0u0%1O1V1x1Y1A1#1D1(1G1+1I191g1:1O1o0s0j000o0z0m0}0W0Y0E0n0s0.0s0v0+0f0n0G0~0Z0Y1T1w1X1z1!1C1%1F0B0t2a1=0Z0#1|1v1~2B1Z1B1$1E1)0I280d0s090u1_0$1d1f1L1j1;1n1p0a1k0M.

  5. Q15. Toute solution de l'équation différentielle \(y' = -y + e^x\) est strictement croissante sur \(\mathbb{R}\).

    • Vrai

    • Faux

    Remarque .+pD1xgsoL)/RP-ueéih mct.0^=(;,{alCnrbyf2}050b040i0F0t0g0h0G0o0w0r0h0I0t0f0q0I0q0J0F0G0p0t0p0g0w0t050g0b0F0$0v0G0F0g0g0A010F0J0r0w0s0u0F0w0p0e0104090B0L0t0A0t0H0p0z0E0n0e0O0t0a0t090M0,0v0E0d0O0E0N0O1n0e090j050k0_0{040x0t0m0h0o0J0@1M0|0~10121416181a1c1e1g0H1j0t0d1I1K1W040D1V0`1X0 11131517191b1d1f1h001-0n1n1p1r1t1v1x0F1z1B1D1F0z1H1J1L1_040:0?0^1_0t0}1{1!1~1%211*240B0y0j260d2b1w1y1A1C1E262I2e2K2h0t020G0w0C0t0y1:2m1N1P0c0#0v1^0{2t1Y1|1#1 1(221g0L2Z1=0t0I000;0?0`0g2t0J0h0r100{1b0U1T2*1`1Z1}1$201)2309200s0K0K0E0l0O2^2n0x1K0Q.

  6. Q16. L'équation \(y' = 0,1y(20 - y)\) admet deux solutions constantes : les fonctions \(y = 0\) et \(y = 20\).

    • Vrai

    • Faux

    Remarque .10003p1xvgsoL)/R-ueiémh ct0.=(,adlnrwyf2050b040i0o0g0t0g0h0D0n0v0p0h0E0P0u0X0g0v0B0E0v0O0t0e0q0F0p0I0p0o0)0t050g0b0(0t0u0D0B0g0g0y010B0/0v0s0r0B0*0d0104090z0H000t0y0t0w090j050k0`0(040A0t0C0X0u0^1r0E0}0 1113150p17191b1d1f0w0A0c0H0z0J0w0t0m0t0H0j1j1l0t090l0p0f0s0%0F0F0h0G1W1Z1m1o1q0{0E040t0h0n1z1^1C10121416181a0o1c1e1g1Z1S1n1p1A040x0t0a1p0L.

  7. Q17. La fonction \(f(x) = e^{-x} + x - 1\) est solution de l'équation \(y' + y = x\).

    • Vrai

    • Faux

    Remarque .10003+Dp1xsOo)/-eihm ct.^=({alnrf}050d040h0A0q0y0q050g0d0y0I0r0z0y0g0g0v010y0B0n0s0o0p0y0s0m0f0104090w0C000w0f0j0q0v0q0l0m0u0x0l0f0D0q0b0q0e090j050k0N0P040t0q0c0i0A0r0L1a0Q0S0U0W0Y0!0$0(0*0,0.0:0=0@130C1x0^0q0w0{0}0 11130e1y1D0|0~10120q0f0`140@0_0f16181k1c0q0a180F.

  8. Q18. Soit \(f\) une solution de \(y' = ay + b\) avec \(a < 0\). On note \(y_0\) la solution constante.

    Affirmation : Si \(f(0) > y_0\), alors la fonction \(f\) est décroissante et convexe sur \(\mathbb{R}\).

    • Vrai

    • Faux

    Remarque .10003DpxvgsoOL)/-ueiéh m_ct0.^=(;,{adlCnrbyf2}050c040j0F0s0g0h0H0n0w0p0h0J0s0v0$0g0w0F0J0w0o0s0o0+0s050g0c0-0(0H0F0g0g0A010F0K0p0w0r0t0F0/0d0104090B0M0u0x0s0A0s0m090N0K0F0v0E0L0P0E0F0P090k050l0_0-040y0s0T0V0X0Z0#0%0f0q0J0q1p0H0:0=0w0@1C0%0v0}0 11131517190o1b1d0B0N0B0d0k1j0s0I0o0z1v0d0P1l0s1n1p1r1t1v1x1z1B0`0J040s0F0e0o0v1W280|0~10121416181a1c1e0I1?1/0x1=0m0s1g1i020f0w0C0s0x1y1A1X1E0s0i0%0U0^2h1Z2j1$2m1)2p1-0N001:1=1k0F1^1`0F1|0s020H2D2F2H271D0s0B0v132g0{2R1#2l1(2o1+2q0B0U2-2/2G262J0;1V2P2|1!2k1%2n1*1,2r2,2C2E382I28040k0D0s0G0$2f3d1Y3f2T303j330N2;3a1U3v0q0v0K0h0p0 0-0/1F0b0:0c0Y0g3u3z2i2~3h2V322X002Z1;1?0F0z0O2(1{1}2B373H3r2@2_0K2{3A2S2 3i2W1e3/0O3m3_393{0o3c1X3#3g2U313k0B2s3^3o3`1D3t3v3x3 4f3C433)1e3G4a2?3J0)0J2d0d0o1F0a1A0R.

  9. Q19. On considère l'équation \((E): y' = 2y - e^{2x}\).

    Affirmation : Toutes les courbes des solutions de \((E)\) possèdent la même tangente au point d'abscisse \(0\).

    • Vrai

    • Faux

    Remarque .+p1x3gsoL)/ueiémh ct.0^q=(,{adlCnEry2}050b040i0C0r0g0h0E0l0t0n0h0G0r0f0o0G0o0I0C0E0m0r0m0g0t0r050g0b0C0Z0s0E0C0g0g0y010C0I0n0t0q0p0C0t0m0d0104090z0J0r0y0r0z0F0r0a0r0d1l0r0c0j0m0w0B0K0d0L090j050k0?0^040u0r0H0Z0=0@0_0{0}0 11131517191b1d1o1h0v1z1B1D0G040A0;1$0r0`0|0~10121416181a1c1e0z0v0j1g0r1k1m0c1!1C1L040-0:1K0^1,1N1/1Q1=1T1^1d0J001{1}1h0K200r0e231$1F0r0i000o0x0l170X0Z0D0,0{0r0t0^0f0m0G180-0/1*1L2b1.1P1;1S1@1V1e1~0z2o1p0e0j1o1m1j1p1r2s251)2z0n1*0t0I0Y0f040D0o0b2L0D0r2E2Q2a1-1O1:1R1?1U1_0F2/1E1#2^2`260z0D0Y0s322F0Q0S0U0W0Y0j0u1B0N.

  10. Q20. Soit \(f\) une solution non nulle de \(y' = ay\).

    Affirmation : Pour tous réels \(x_1\) et \(x_2\), \(f(x_1 + x_2) = f(x_1) \times f(x_2)\) si et seulement si \(f(0) = 1\).

    • Vrai

    • Faux

    Remarque .10003+p1xvgsàoOL)/ueiéh m_ct.q^0=(,{adlCnrf2}050c040l0G0t0h0j0I0o0x0q0j0K0t0p0h0x0t050h0c0G0$0w0I0G0h0h0C010G0L0q0x0s0u0G0x0p0e0104090D0M0D0e0m0t0C0t0J0p0A0F0G0e0O090m050n0-0/040y0t0k0$0T0,0.0:0=0@0_0{0}0 11131517190e0v0d0t0b0t1N0N1c1e1g1i0G1a1O1Q1S0v1U1m1o1q1A040%0*1z0/0t0;0?0^0`0|0~10121416181!0d0m1M1(1V1f0A0N1h1j221$1T0m1*1p1r0K1t0t0l000r0g0G0I0}0r0+2j1?1C1_1F1|1I1 1L2d1R2f1d0t2523251U1n2i1-0t0r0z0o0q0f0G0Y0t0i2v1A2x1^1E1{1H1~1K0D0J2I0J292O1,1s0E0U0j0}2#1=1@1D1`1G1}1J202/1e0B2?2j1.0j0o2}1B2(312B2,352I0d391-1u0J0j0u0u0p3e2%302A2+341L3n1s0%0)0t0K0#3G0o0I0I0p2_1;3f3x2*332D2.3l3C2k2_0H0#0w3v2 2z3S2C2-190B273m1+3a1u0a1p0Q.

Vrai / Faux — Équations Différentielles Série 2

  1. Q11. Soit \((E): y' + 3y = 6\). La solution \(f\) de \((E)\) telle que \(f(0) = 5\) est définie par \(f(x) = 3e^{-3x} + 2\).

    • Vrai

    • Faux

    Remarque .10003+pDx35vgsoL)/-ueéih mAct.0^=(,{adlCnEryf2}050c040l0G0u0j0k0I0p0y0s0k0K0u0i0r0K0r0M0G0I0q0u0H0;050j0c0G0(0x0I0G0j0j0C010G0M0s0y0t0v0G0y0q0e0104090D0D0L0m090m050n0_0{040u0q0j0y0u0^0`0|0~10121416181a1c1e1g0N0u0C0u0J0q0B0F0o0f0e0Q0u0b0u0P1l1n1p0K040z0u0w0h0q0x1w1$0u0}0 11131517191b1d1f0D0O0D0A0m1L0u0g1!1o1y040E0u0%0u0y0M0k0p1,1/1y1;1A1@1D1`1G1}1g0J240f271$1(0u0d0%1.1x0{2m1?1C1_1F1|1I1 0D0e231M0f1P1R1T1V1X1Z1m281q1)0a1n0S.

  2. Q12. Soit \(f\) une solution de \(y' = -2y + 8\).

    Affirmation : La limite de \(f\) en \(+\infty\) dépend de la condition initiale \(f(0)\).

    • Vrai

    • Faux

    Remarque .+pxQvgsoL)/-ueéih mct.q^0=(,{adl4Cnryf2}050b040i0D0r0g0h0F0m0u0p0h0I0r0f0o0I0o0J0D0F0n0r0n0g0u0r050g0b0D0#0t0F0D0g0g0z010D0J0p0u0q0s0D0u0n0c0104090A0L0A0c0j0r0z0r0H0n0x0C0l0M0c0N0r0a0r0G090j050k0^0`040v0r0d0m0`0E0?1E0{0}0 11131517191b1d1f0c0r090u0h1w090p0I0L0u0K1A1C1O040B1N0_1P0~10121416181a1c1e1g1i1k1$1(1z1B1D1_041N0u0J0!0f040w0m0n0F0-0r2k0.0U151;2f2h2d0}0r0e0,0n0m0J0r0E0.0@1_0r0|1{1S1~1V211Y0A0H1:2b1F0r0A0E0!0t2F2H1O2K1Q1|1T1 1W221f1h0y0j2U1=0j0v1C0P.

  3. Q13. On considère l'équation \(y' = ay\). Si \(f(0) = 1\) et \(f(1) = e^2\), alors \(a = 2\).

    • Vrai

    • Faux

    Remarque .10003p1xvsoL)/ueéimh Act.0^=(,{alnrbf2}050b040h0B0q0f0g0C0k0t0n0g0D0q0l0f0t0q050f0b0B0W0s0C0B0f0f0x010B0E0n0t0p0o0B0t0l0d0104090y0G0y0d0i0q0x0X0w0A0B0d0I090i050j0%0)040u0q0r0e0l0s0#1j0*0,0.0:0=0@0_0{0}0 11130v16180c1f1h1t040q0y0e0m0?0G0n0m160l0!0$0(1u0-0/0;0?0^0`0|0~10120y0c1H190N180l0w0H1K1i1!040z0q0V210F0T0l0D1Y1t0q0+1$1x1)1A1,1D0y1@0q1{1g1}1k1m0a1h0K.

  4. Q14. Soit \(f\) la solution de \(y' = y - 1\) passant par le point \(A(0;2)\).

    Affirmation : La tangente à la courbe de \(f\) au point \(A\) a pour équation \(y = x + 2\).

    • Vrai

    • Faux

    Remarque .10003+p1xgsoOL)/ueéimh Act.0^q=(,adlnryf2050c040j0D0s0g0h0F0m0v0p0h0G0s0n0g0v0s050g0c0D0Y0u0F0D0g0g0A010D0H0p0v0r0q0D0v0n0e0104090B0J0B0e0k0s0A0Z0y0e0s0b0s0d090k050l0)0+040w0s0i0Y0P0(0*0,0.0:0=0@0_0{0}0 1113150x181a0K1i1k1m0G040Z0$1u0+0s0-0/0;0?0^0`0|0~10121400161J1b0e1M1l1v040C0s0E0X0u0%1O1V1x1Y1A1#1D1(1G1+1I191g1:1O1o0s0j000o0z0m0}0W0Y0E0n0s0.0s0v0+0f0n0G0~0Z0Y1T1w1X1z1!1C1%1F0B0t2a1=0Z0#1|1v1~2B1Z1B1$1E1)0I280d0s090u1_0$1d1f1L1j1;1n1p0a1k0M.

  5. Q15. Toute solution de l'équation différentielle \(y' = -y + e^x\) est strictement croissante sur \(\mathbb{R}\).

    • Vrai

    • Faux

    Remarque .+pD1xgsoL)/RP-ueéih mct.0^=(;,{alCnrbyf2}050b040i0F0t0g0h0G0o0w0r0h0I0t0f0q0I0q0J0F0G0p0t0p0g0w0t050g0b0F0$0v0G0F0g0g0A010F0J0r0w0s0u0F0w0p0e0104090B0L0t0A0t0H0p0z0E0n0e0O0t0a0t090M0,0v0E0d0O0E0N0O1n0e090j050k0_0{040x0t0m0h0o0J0@1M0|0~10121416181a1c1e1g0H1j0t0d1I1K1W040D1V0`1X0 11131517191b1d1f1h001-0n1n1p1r1t1v1x0F1z1B1D1F0z1H1J1L1_040:0?0^1_0t0}1{1!1~1%211*240B0y0j260d2b1w1y1A1C1E262I2e2K2h0t020G0w0C0t0y1:2m1N1P0c0#0v1^0{2t1Y1|1#1 1(221g0L2Z1=0t0I000;0?0`0g2t0J0h0r100{1b0U1T2*1`1Z1}1$201)2309200s0K0K0E0l0O2^2n0x1K0Q.

  6. Q16. L'équation \(y' = 0,1y(20 - y)\) admet deux solutions constantes : les fonctions \(y = 0\) et \(y = 20\).

    • Vrai

    • Faux

    Remarque .10003p1xvgsoL)/R-ueiémh ct0.=(,adlnrwyf2050b040i0o0g0t0g0h0D0n0v0p0h0E0P0u0X0g0v0B0E0v0O0t0e0q0F0p0I0p0o0)0t050g0b0(0t0u0D0B0g0g0y010B0/0v0s0r0B0*0d0104090z0H000t0y0t0w090j050k0`0(040A0t0C0X0u0^1r0E0}0 1113150p17191b1d1f0w0A0c0H0z0J0w0t0m0t0H0j1j1l0t090l0p0f0s0%0F0F0h0G1W1Z1m1o1q0{0E040t0h0n1z1^1C10121416181a0o1c1e1g1Z1S1n1p1A040x0t0a1p0L.

  7. Q17. La fonction \(f(x) = e^{-x} + x - 1\) est solution de l'équation \(y' + y = x\).

    • Vrai

    • Faux

    Remarque .10003+Dp1xsOo)/-eihm ct.^=({alnrf}050d040h0A0q0y0q050g0d0y0I0r0z0y0g0g0v010y0B0n0s0o0p0y0s0m0f0104090w0C000w0f0j0q0v0q0l0m0u0x0l0f0D0q0b0q0e090j050k0N0P040t0q0c0i0A0r0L1a0Q0S0U0W0Y0!0$0(0*0,0.0:0=0@130C1x0^0q0w0{0}0 11130e1y1D0|0~10120q0f0`140@0_0f16181k1c0q0a180F.

  8. Q18. Soit \(f\) une solution de \(y' = ay + b\) avec \(a < 0\). On note \(y_0\) la solution constante.

    Affirmation : Si \(f(0) > y_0\), alors la fonction \(f\) est décroissante et convexe sur \(\mathbb{R}\).

    • Vrai

    • Faux

    Remarque .10003DpxvgsoOL)/-ueiéh m_ct0.^=(;,{adlCnrbyf2}050c040j0F0s0g0h0H0n0w0p0h0J0s0v0$0g0w0F0J0w0o0s0o0+0s050g0c0-0(0H0F0g0g0A010F0K0p0w0r0t0F0/0d0104090B0M0u0x0s0A0s0m090N0K0F0v0E0L0P0E0F0P090k050l0_0-040y0s0T0V0X0Z0#0%0f0q0J0q1p0H0:0=0w0@1C0%0v0}0 11131517190o1b1d0B0N0B0d0k1j0s0I0o0z1v0d0P1l0s1n1p1r1t1v1x1z1B0`0J040s0F0e0o0v1W280|0~10121416181a1c1e0I1?1/0x1=0m0s1g1i020f0w0C0s0x1y1A1X1E0s0i0%0U0^2h1Z2j1$2m1)2p1-0N001:1=1k0F1^1`0F1|0s020H2D2F2H271D0s0B0v132g0{2R1#2l1(2o1+2q0B0U2-2/2G262J0;1V2P2|1!2k1%2n1*1,2r2,2C2E382I28040k0D0s0G0$2f3d1Y3f2T303j330N2;3a1U3v0q0v0K0h0p0 0-0/1F0b0:0c0Y0g3u3z2i2~3h2V322X002Z1;1?0F0z0O2(1{1}2B373H3r2@2_0K2{3A2S2 3i2W1e3/0O3m3_393{0o3c1X3#3g2U313k0B2s3^3o3`1D3t3v3x3 4f3C433)1e3G4a2?3J0)0J2d0d0o1F0a1A0R.

  9. Q19. On considère l'équation \((E): y' = 2y - e^{2x}\).

    Affirmation : Toutes les courbes des solutions de \((E)\) possèdent la même tangente au point d'abscisse \(0\).

    • Vrai

    • Faux

    Remarque .+p1x3gsoL)/ueiémh ct.0^q=(,{adlCnEry2}050b040i0C0r0g0h0E0l0t0n0h0G0r0f0o0G0o0I0C0E0m0r0m0g0t0r050g0b0C0Z0s0E0C0g0g0y010C0I0n0t0q0p0C0t0m0d0104090z0J0r0y0r0z0F0r0a0r0d1l0r0c0j0m0w0B0K0d0L090j050k0?0^040u0r0H0Z0=0@0_0{0}0 11131517191b1d1o1h0v1z1B1D0G040A0;1$0r0`0|0~10121416181a1c1e0z0v0j1g0r1k1m0c1!1C1L040-0:1K0^1,1N1/1Q1=1T1^1d0J001{1}1h0K200r0e231$1F0r0i000o0x0l170X0Z0D0,0{0r0t0^0f0m0G180-0/1*1L2b1.1P1;1S1@1V1e1~0z2o1p0e0j1o1m1j1p1r2s251)2z0n1*0t0I0Y0f040D0o0b2L0D0r2E2Q2a1-1O1:1R1?1U1_0F2/1E1#2^2`260z0D0Y0s322F0Q0S0U0W0Y0j0u1B0N.

  10. Q20. Soit \(f\) une solution non nulle de \(y' = ay\).

    Affirmation : Pour tous réels \(x_1\) et \(x_2\), \(f(x_1 + x_2) = f(x_1) \times f(x_2)\) si et seulement si \(f(0) = 1\).

    • Vrai

    • Faux

    Remarque .10003+p1xvgsàoOL)/ueiéh m_ct.q^0=(,{adlCnrf2}050c040l0G0t0h0j0I0o0x0q0j0K0t0p0h0x0t050h0c0G0$0w0I0G0h0h0C010G0L0q0x0s0u0G0x0p0e0104090D0M0D0e0m0t0C0t0J0p0A0F0G0e0O090m050n0-0/040y0t0k0$0T0,0.0:0=0@0_0{0}0 11131517190e0v0d0t0b0t1N0N1c1e1g1i0G1a1O1Q1S0v1U1m1o1q1A040%0*1z0/0t0;0?0^0`0|0~10121416181!0d0m1M1(1V1f0A0N1h1j221$1T0m1*1p1r0K1t0t0l000r0g0G0I0}0r0+2j1?1C1_1F1|1I1 1L2d1R2f1d0t2523251U1n2i1-0t0r0z0o0q0f0G0Y0t0i2v1A2x1^1E1{1H1~1K0D0J2I0J292O1,1s0E0U0j0}2#1=1@1D1`1G1}1J202/1e0B2?2j1.0j0o2}1B2(312B2,352I0d391-1u0J0j0u0u0p3e2%302A2+341L3n1s0%0)0t0K0#3G0o0I0I0p2_1;3f3x2*332D2.3l3C2k2_0H0#0w3v2 2z3S2C2-190B273m1+3a1u0a1p0Q.