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 .10003d/Ey,)A3} oxepuafsnghct.mvL+D(=52réC{0l^-i050o040B0q0k0s0l0N0p0x0Q0l0t0k0u0J0t0J0I0q0N0n0k0b0;050s0o0q0(0w0N0q0s0s0F010q0I0Q0x0v0z0q0x0n0m0104090E0E0d0g090g050c0_0{040k0n0s0x0k0^0`0|0~10121416181a1c1e1g0e0k0F0k0K0n0O0L0P0i0m0j0k0C0k0H1l1n1p0t040y0k0h0A0n0w1w1$0k0}0 11131517191b1d1f0E0r0E0M0g1L0k0G1!1o1y040f0k0%0k0x0I0l0p1,1/1y1;1A1@1D1`1G1}1g0K240i271$1(0k0D0%1.1x0{2m1?1C1_1F1|1I1 0E0m231M0i1P1R1T1V1X1Z1m281q1)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 .d/yq4,)} oxepuafsnghct.mvL+Q(=2réC{0l^-i050m040z0o0i0q0j0K0n0v0N0j0r0i0s0G0r0G0F0o0K0l0i0l0q0v0i050q0m0o0#0u0K0o0q0q0D010o0F0N0v0t0x0o0v0l0k0104090C0p0C0k0g0i0D0i0H0l0L0I0M0E0k0h0i0A0i0e090g050b0^0`040w0i0B0n0`0a0?1E0{0}0 11131517191b1d1f0k0i090v0j1w090N0r0p0v0c1A1C1O040f1N0_1P0~10121416181a1c1e1g1i1k1$1(1z1B1D1_041N0v0F0!0s040d0n0l0K0-0i2k0.0U151;2f2h2d0}0i0y0,0l0n0F0i0a0.0@1_0i0|1{1S1~1V211Y0C0H1:2b1F0i0C0a0!0u2F2H1O2K1Q1|1T1 1W221f1h0J0g2U1=0g0w1C0P.

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

    • Vrai

    • Faux

    Remarque .10003/,)A} oxbepuaf1snhct.mvL(=2r0{él^i050l040y0n0g0q0h0G0m0u0I0h0r0g0k0q0u0g050q0l0n0W0t0G0n0q0q0A010n0C0I0u0s0w0n0u0k0i0104090z0o0z0i0d0g0A0X0H0E0n0i0f090d050b0%0)040v0g0e0x0k0t0#1j0*0,0.0:0=0@0_0{0}0 11130D16180p1f1h1t040g0z0x0F0?0o0I0F160k0!0$0(1u0-0/0;0?0^0`0|0~10120z0p1H190N180k0H0B1K1i1!040c0g0V210j0T0k0r1Y1t0g0+1$1x1)1A1,1D0z1@0g1{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 .10003d/yq,)A oxepuaf1snghct.mOL+(=2r0él^i050m040A0o0i0r0j0I0n0w0K0j0s0i0l0r0w0i050r0m0o0Y0v0I0o0r0r0D010o0F0K0w0u0y0o0w0l0k0104090C0p0C0k0g0i0D0Z0J0k0i0B0i0q090g050c0)0+040x0i0z0Y0P0(0*0,0.0:0=0@0_0{0}0 1113150G181a0E1i1k1m0s040Z0$1u0+0i0-0/0;0?0^0`0|0~10121400161J1b0k1M1l1v040f0i0b0X0v0%1O1V1x1Y1A1#1D1(1G1+1I191g1:1O1o0i0A000H0e0n0}0W0Y0b0l0i0.0i0w0+0t0l0s0~0Z0Y1T1w1X1z1!1C1%1F0C0h2a1=0Z0#1|1v1~2B1Z1B1$1E1)0d280q0i090v1_0$1d1f1L1j1;1n1p0a1k0M.

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

    • Vrai

    • Faux

    Remarque ./y,)P} oxbepuaf1snghct.mL+;D(=R2réC{0l^-i050l040y0n0g0q0h0L0m0v0O0h0r0g0s0H0r0H0G0n0L0k0g0k0q0v0g050q0l0n0$0u0L0n0q0q0D010n0G0O0v0t0x0n0v0k0i0104090C0b0g0D0g0I0k0M0J0N0i0f0g0z0g090o0,0u0J0p0f0J0F0f1n0i090d050a0_0{040w0g0e0h0m0G0@1M0|0~10121416181a1c1e1g0I1j0g0p1I1K1W040c1V0`1X0 11131517191b1d1f1h001-0N1n1p1r1t1v1x0n1z1B1D1F0M1H1J1L1_040:0?0^1_0g0}1{1!1~1%211*240C0K0d260p2b1w1y1A1C1E262I2e2K2h0g020L0v0A0g0K1:2m1N1P0B0#0u1^0{2t1Y1|1#1 1(221g0b2Z1=0g0r000;0?0`0q2t0G0h0O100{1b0U1T2*1`1Z1}1$201)2309200t0j0j0J0E0f2^2n0w1K0Q.

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

    • Vrai

    • Faux

    Remarque .10003d/y,) oxepuaf1snghct.mvL(=wR2ré0l-i050k040y0j0p0g0p0h0H0l0u0J0h0q0P0t0X0p0u0m0q0u0O0g0x0F0E0J0n0J0j0)0g050p0k0(0g0t0H0m0p0p0A010m0/0u0s0w0m0*0i0104090z0d000g0A0g0G090f050c0`0(040e0g0b0X0t0^1r0q0}0 1113150J17191b1d1f0G0e0o0d0z0D0G0g0I0g0d0f1j1l0g090C0J0r0s0%0E0E0h0B1W1Z1m1o1q0{0q040g0h0l1z1^1C10121416181a0j1c1e1g1Z1S1n1p1A040v0g0a1p0L.

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

    • Vrai

    • Faux

    Remarque .10003/)} xoepaf1snhct.mO+D(=r{l^-i050i040t0n0e0j0e050m0i0j0I0p0A0j0m0m0x010j0y0D0q0o0s0j0q0h0f0104090w0k000w0f0c0e0x0e0C0h0B0z0C0f0d0e0u0e0l090c050b0N0P040r0e0v0g0n0p0L1a0Q0S0U0W0Y0!0$0(0*0,0.0:0=0@130k1x0^0e0w0{0}0 11130l1y1D0|0~10120e0f0`140@0_0f16181k1c0e0a180F.

  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 .10003d/y,)} oxbepuafsnghct.m_vOL;D(=2r0{éCl^-i050m040B0o0h0q0i0M0n0v0P0i0r0h0u0$0q0v0o0r0v0l0h0l0+0h050q0m0-0(0M0o0q0q0F010o0H0P0v0t0x0o0/0j0104090E0d0y0I0h0F0h0O090p0H0o0u0J0k0g0J0o0g090f050c0_0-040w0h0T0V0X0Z0#0%0s0K0r0K1p0M0:0=0v0@1C0%0u0}0 11131517190l1b1d0E0p0E0j0f1j0h0L0l0N1v0j0g1l0h1n1p1r1t1v1x1z1B0`0r040h0o0z0l0u1W280|0~10121416181a1c1e0L1?1/0I1=0O0h1g1i020s0v0C0h0I1y1A1X1E0h0A0%0U0^2h1Z2j1$2m1)2p1-0p001:1=1k0o1^1`0o1|0h020M2D2F2H271D0h0E0u132g0{2R1#2l1(2o1+2q0E0U2-2/2G262J0;1V2P2|1!2k1%2n1*1,2r2,2C2E382I28040f0e0h0b0$2f3d1Y3f2T303j330p2;3a1U3v0K0u0H0i0P0 0-0/1F0D0:0m0Y0q3u3z2i2~3h2V322X002Z1;1?0o0N0G2(1{1}2B373H3r2@2_0H2{3A2S2 3i2W1e3/0G3m3_393{0l3c1X3#3g2U313k0E2s3^3o3`1D3t3v3x3 4f3C433)1e3G4a2?3J0)0r2d0j0l1F0a1A0R.

  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 .d/Eyq,)3} oxepua1snghct.mL+(=2réC{0l^i050n040z0p0j0r0k0J0o0w0L0k0s0j0t0F0s0F0E0p0J0m0j0m0r0w0j050r0n0p0Z0v0J0p0r0r0C010p0E0L0w0u0y0p0w0m0l0104090B0d0j0C0j0B0G0j0A0j0l1l0j0q0g0m0K0H0D0l0i090g050b0?0^040x0j0c0Z0=0@0_0{0}0 11131517191b1d1o1h0I1z1B1D0s040f0;1$0j0`0|0~10121416181a1c1e0B0I0g1g0j1k1m0q1!1C1L040-0:1K0^1,1N1/1Q1=1T1^1d0d001{1}1h0D200j0h231$1F0j0z000F0e0o170X0Z0a0,0{0j0w0^0t0m0s180-0/1*1L2b1.1P1;1S1@1V1e1~0B2o1p0h0g1o1m1j1p1r2s251)2z0L1*0w0E0Y0t040a0F0n2L0a0j2E2Q2a1-1O1:1R1?1U1_0G2/1E1#2^2`260B0a0Y0v322F0Q0S0U0W0Y0g0x1B0N.

  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 .10003d/q,)} oxepuaf1snghct.m_OvL+(=2rC{é0l^ià050l040B0n0h0q0i0L0m0v0N0i0r0h0k0q0v0h050q0l0n0$0u0L0n0q0q0E010n0G0N0v0t0x0n0v0k0j0104090D0o0D0j0f0h0E0h0H0k0M0I0n0j0g090f050c0-0/040w0h0z0$0T0,0.0:0=0@0_0{0}0 11131517190j0y0p0h0C0h1N0F1c1e1g1i0n1a1O1Q1S0y1U1m1o1q1A040%0*1z0/0h0;0?0^0`0|0~10121416181!0p0f1M1(1V1f0M0F1h1j221$1T0f1*1p1r0r1t0h0B000J0s0n0L0}0J0+2j1?1C1_1F1|1I1 1L2d1R2f1d0h2523251U1n2i1-0h0J0d0m0N0A0n0Y0h0O2v1A2x1^1E1{1H1~1K0D0H2I0H292O1,1s0e0U0i0}2#1=1@1D1`1G1}1J202/1e0K2?2j1.0i0m2}1B2(312B2,352I0p391-1u0H0i0x0x0k3e2%302A2+341L3n1s0%0)0h0r0#3G0m0L0L0k2_1;3f3x2*332D2.3l3C2k2_0b0#0u3v2 2z3S2C2-190K273m1+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 .10003d/Ey,)A3} oxepuafsnghct.mvL+D(=52réC{0l^-i050o040B0q0k0s0l0N0p0x0Q0l0t0k0u0J0t0J0I0q0N0n0k0b0;050s0o0q0(0w0N0q0s0s0F010q0I0Q0x0v0z0q0x0n0m0104090E0E0d0g090g050c0_0{040k0n0s0x0k0^0`0|0~10121416181a1c1e1g0e0k0F0k0K0n0O0L0P0i0m0j0k0C0k0H1l1n1p0t040y0k0h0A0n0w1w1$0k0}0 11131517191b1d1f0E0r0E0M0g1L0k0G1!1o1y040f0k0%0k0x0I0l0p1,1/1y1;1A1@1D1`1G1}1g0K240i271$1(0k0D0%1.1x0{2m1?1C1_1F1|1I1 0E0m231M0i1P1R1T1V1X1Z1m281q1)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 .d/yq4,)} oxepuafsnghct.mvL+Q(=2réC{0l^-i050m040z0o0i0q0j0K0n0v0N0j0r0i0s0G0r0G0F0o0K0l0i0l0q0v0i050q0m0o0#0u0K0o0q0q0D010o0F0N0v0t0x0o0v0l0k0104090C0p0C0k0g0i0D0i0H0l0L0I0M0E0k0h0i0A0i0e090g050b0^0`040w0i0B0n0`0a0?1E0{0}0 11131517191b1d1f0k0i090v0j1w090N0r0p0v0c1A1C1O040f1N0_1P0~10121416181a1c1e1g1i1k1$1(1z1B1D1_041N0v0F0!0s040d0n0l0K0-0i2k0.0U151;2f2h2d0}0i0y0,0l0n0F0i0a0.0@1_0i0|1{1S1~1V211Y0C0H1:2b1F0i0C0a0!0u2F2H1O2K1Q1|1T1 1W221f1h0J0g2U1=0g0w1C0P.

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

    • Vrai

    • Faux

    Remarque .10003/,)A} oxbepuaf1snhct.mvL(=2r0{él^i050l040y0n0g0q0h0G0m0u0I0h0r0g0k0q0u0g050q0l0n0W0t0G0n0q0q0A010n0C0I0u0s0w0n0u0k0i0104090z0o0z0i0d0g0A0X0H0E0n0i0f090d050b0%0)040v0g0e0x0k0t0#1j0*0,0.0:0=0@0_0{0}0 11130D16180p1f1h1t040g0z0x0F0?0o0I0F160k0!0$0(1u0-0/0;0?0^0`0|0~10120z0p1H190N180k0H0B1K1i1!040c0g0V210j0T0k0r1Y1t0g0+1$1x1)1A1,1D0z1@0g1{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 .10003d/yq,)A oxepuaf1snghct.mOL+(=2r0él^i050m040A0o0i0r0j0I0n0w0K0j0s0i0l0r0w0i050r0m0o0Y0v0I0o0r0r0D010o0F0K0w0u0y0o0w0l0k0104090C0p0C0k0g0i0D0Z0J0k0i0B0i0q090g050c0)0+040x0i0z0Y0P0(0*0,0.0:0=0@0_0{0}0 1113150G181a0E1i1k1m0s040Z0$1u0+0i0-0/0;0?0^0`0|0~10121400161J1b0k1M1l1v040f0i0b0X0v0%1O1V1x1Y1A1#1D1(1G1+1I191g1:1O1o0i0A000H0e0n0}0W0Y0b0l0i0.0i0w0+0t0l0s0~0Z0Y1T1w1X1z1!1C1%1F0C0h2a1=0Z0#1|1v1~2B1Z1B1$1E1)0d280q0i090v1_0$1d1f1L1j1;1n1p0a1k0M.

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

    • Vrai

    • Faux

    Remarque ./y,)P} oxbepuaf1snghct.mL+;D(=R2réC{0l^-i050l040y0n0g0q0h0L0m0v0O0h0r0g0s0H0r0H0G0n0L0k0g0k0q0v0g050q0l0n0$0u0L0n0q0q0D010n0G0O0v0t0x0n0v0k0i0104090C0b0g0D0g0I0k0M0J0N0i0f0g0z0g090o0,0u0J0p0f0J0F0f1n0i090d050a0_0{040w0g0e0h0m0G0@1M0|0~10121416181a1c1e1g0I1j0g0p1I1K1W040c1V0`1X0 11131517191b1d1f1h001-0N1n1p1r1t1v1x0n1z1B1D1F0M1H1J1L1_040:0?0^1_0g0}1{1!1~1%211*240C0K0d260p2b1w1y1A1C1E262I2e2K2h0g020L0v0A0g0K1:2m1N1P0B0#0u1^0{2t1Y1|1#1 1(221g0b2Z1=0g0r000;0?0`0q2t0G0h0O100{1b0U1T2*1`1Z1}1$201)2309200t0j0j0J0E0f2^2n0w1K0Q.

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

    • Vrai

    • Faux

    Remarque .10003d/y,) oxepuaf1snghct.mvL(=wR2ré0l-i050k040y0j0p0g0p0h0H0l0u0J0h0q0P0t0X0p0u0m0q0u0O0g0x0F0E0J0n0J0j0)0g050p0k0(0g0t0H0m0p0p0A010m0/0u0s0w0m0*0i0104090z0d000g0A0g0G090f050c0`0(040e0g0b0X0t0^1r0q0}0 1113150J17191b1d1f0G0e0o0d0z0D0G0g0I0g0d0f1j1l0g090C0J0r0s0%0E0E0h0B1W1Z1m1o1q0{0q040g0h0l1z1^1C10121416181a0j1c1e1g1Z1S1n1p1A040v0g0a1p0L.

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

    • Vrai

    • Faux

    Remarque .10003/)} xoepaf1snhct.mO+D(=r{l^-i050i040t0n0e0j0e050m0i0j0I0p0A0j0m0m0x010j0y0D0q0o0s0j0q0h0f0104090w0k000w0f0c0e0x0e0C0h0B0z0C0f0d0e0u0e0l090c050b0N0P040r0e0v0g0n0p0L1a0Q0S0U0W0Y0!0$0(0*0,0.0:0=0@130k1x0^0e0w0{0}0 11130l1y1D0|0~10120e0f0`140@0_0f16181k1c0e0a180F.

  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 .10003d/y,)} oxbepuafsnghct.m_vOL;D(=2r0{éCl^-i050m040B0o0h0q0i0M0n0v0P0i0r0h0u0$0q0v0o0r0v0l0h0l0+0h050q0m0-0(0M0o0q0q0F010o0H0P0v0t0x0o0/0j0104090E0d0y0I0h0F0h0O090p0H0o0u0J0k0g0J0o0g090f050c0_0-040w0h0T0V0X0Z0#0%0s0K0r0K1p0M0:0=0v0@1C0%0u0}0 11131517190l1b1d0E0p0E0j0f1j0h0L0l0N1v0j0g1l0h1n1p1r1t1v1x1z1B0`0r040h0o0z0l0u1W280|0~10121416181a1c1e0L1?1/0I1=0O0h1g1i020s0v0C0h0I1y1A1X1E0h0A0%0U0^2h1Z2j1$2m1)2p1-0p001:1=1k0o1^1`0o1|0h020M2D2F2H271D0h0E0u132g0{2R1#2l1(2o1+2q0E0U2-2/2G262J0;1V2P2|1!2k1%2n1*1,2r2,2C2E382I28040f0e0h0b0$2f3d1Y3f2T303j330p2;3a1U3v0K0u0H0i0P0 0-0/1F0D0:0m0Y0q3u3z2i2~3h2V322X002Z1;1?0o0N0G2(1{1}2B373H3r2@2_0H2{3A2S2 3i2W1e3/0G3m3_393{0l3c1X3#3g2U313k0E2s3^3o3`1D3t3v3x3 4f3C433)1e3G4a2?3J0)0r2d0j0l1F0a1A0R.

  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 .d/Eyq,)3} oxepua1snghct.mL+(=2réC{0l^i050n040z0p0j0r0k0J0o0w0L0k0s0j0t0F0s0F0E0p0J0m0j0m0r0w0j050r0n0p0Z0v0J0p0r0r0C010p0E0L0w0u0y0p0w0m0l0104090B0d0j0C0j0B0G0j0A0j0l1l0j0q0g0m0K0H0D0l0i090g050b0?0^040x0j0c0Z0=0@0_0{0}0 11131517191b1d1o1h0I1z1B1D0s040f0;1$0j0`0|0~10121416181a1c1e0B0I0g1g0j1k1m0q1!1C1L040-0:1K0^1,1N1/1Q1=1T1^1d0d001{1}1h0D200j0h231$1F0j0z000F0e0o170X0Z0a0,0{0j0w0^0t0m0s180-0/1*1L2b1.1P1;1S1@1V1e1~0B2o1p0h0g1o1m1j1p1r2s251)2z0L1*0w0E0Y0t040a0F0n2L0a0j2E2Q2a1-1O1:1R1?1U1_0G2/1E1#2^2`260B0a0Y0v322F0Q0S0U0W0Y0g0x1B0N.

  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 .10003d/q,)} oxepuaf1snghct.m_OvL+(=2rC{é0l^ià050l040B0n0h0q0i0L0m0v0N0i0r0h0k0q0v0h050q0l0n0$0u0L0n0q0q0E010n0G0N0v0t0x0n0v0k0j0104090D0o0D0j0f0h0E0h0H0k0M0I0n0j0g090f050c0-0/040w0h0z0$0T0,0.0:0=0@0_0{0}0 11131517190j0y0p0h0C0h1N0F1c1e1g1i0n1a1O1Q1S0y1U1m1o1q1A040%0*1z0/0h0;0?0^0`0|0~10121416181!0p0f1M1(1V1f0M0F1h1j221$1T0f1*1p1r0r1t0h0B000J0s0n0L0}0J0+2j1?1C1_1F1|1I1 1L2d1R2f1d0h2523251U1n2i1-0h0J0d0m0N0A0n0Y0h0O2v1A2x1^1E1{1H1~1K0D0H2I0H292O1,1s0e0U0i0}2#1=1@1D1`1G1}1J202/1e0K2?2j1.0i0m2}1B2(312B2,352I0p391-1u0H0i0x0x0k3e2%302A2+341L3n1s0%0)0h0r0#3G0m0L0L0k2_1;3f3x2*332D2.3l3C2k2_0b0#0u3v2 2z3S2C2-190K273m1+3a1u0a1p0Q.