4.10.18 Problems 1701 to 1800

Table 4.1051: System of differential equations

#

ODE

Mathematica

Maple

Sympy

23714

\[ {} [x^{\prime }\left (t \right ) = a \left (b -x \left (t \right )\right )-c f y \left (t \right ), y^{\prime }\left (t \right ) = d \left (x \left (t \right )-y \left (t \right )\right )-c f y \left (t \right )-a y \left (t \right )] \]

23715

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right )] \]

23716

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )] \]

23717

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )] \]

23718

\[ {} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )] \]

23719

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 17 x \left (t \right )-7 y \left (t \right )] \]

23720

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )] \]

23721

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )] \]

23722

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )] \]

23723

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 12 x \left (t \right )-7 y \left (t \right )] \]

23724

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )] \]

23725

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )] \]

23726

\[ {} [x^{\prime }\left (t \right ) = 4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

23727

\[ {} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )] \]

23728

\[ {} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )] \]

23729

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

23730

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

23731

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-4 y \left (t \right )-z \left (t \right )] \]

23732

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+3 z \left (t \right )] \]

23733

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right )] \]

23734

\[ {} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )-4 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-8 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right )-8 z \left (t \right )] \]

23735

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right )-w \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+2 z \left (t \right )+2 w \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+2 w \left (t \right ), w^{\prime }\left (t \right ) = -3 y \left (t \right )-6 z \left (t \right )-6 w \left (t \right )] \]

23736

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), z^{\prime }\left (t \right ) = 2 z \left (t \right )+w \left (t \right )+h \left (t \right ), w^{\prime }\left (t \right ) = z \left (t \right )+2 w \left (t \right )+h \left (t \right ), h^{\prime }\left (t \right ) = z \left (t \right )+w \left (t \right )+2 h \left (t \right )] \]

23737

\[ {} [x^{\prime }\left (t \right ) = -10 x \left (t \right )+y \left (t \right )+7 z \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+4 y \left (t \right )+5 z \left (t \right ), z^{\prime }\left (t \right ) = -17 x \left (t \right )+y \left (t \right )+12 z \left (t \right )] \]

23738

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )] \]

23739

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-4 y \left (t \right )-z \left (t \right )] \]

23740

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+3 z \left (t \right )] \]

23741

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right )] \]

23742

\[ {} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )-4 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-8 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right )-8 z \left (t \right )] \]

23743

\[ {} [x^{\prime }\left (t \right ) = -10 x \left (t \right )+y \left (t \right )+7 z \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+4 y \left (t \right )+5 z \left (t \right ), z^{\prime }\left (t \right ) = -17 x \left (t \right )+y \left (t \right )+12 z \left (t \right )] \]

23744

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )] \]

23745

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-5 z \left (t \right ), u^{\prime }\left (t \right ) = 5 z \left (t \right )] \]

23881

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )] \]

23882

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )] \]

23883

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

23884

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

23885

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )] \]

23886

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )] \]

23887

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )] \]

23888

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )] \]

23889

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )] \]

23890

\[ {} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

23891

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right )^{2}-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )] \]

23892

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -\sin \left (x \left (t \right )\right )] \]

23893

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -4 \sin \left (x \left (t \right )\right )] \]

23894

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )] \]

23895

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )] \]

23896

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = \sin \left (x_{1} \left (t \right )\right )] \]

23897

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )] \]

23898

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{1} \left (t \right )^{3}] \]

23899

\[ {} [x^{\prime }\left (t \right ) = a x \left (t \right )+b y \left (t \right ), y^{\prime }\left (t \right ) = c x \left (t \right )+d y \left (t \right )] \]

23900

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

23901

\[ {} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

23902

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )] \]

23903

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )] \]

23904

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )] \]

23905

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right )] \]

23906

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )] \]

23907

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )] \]

23908

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]

23909

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )] \]

23910

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-10 y \left (t \right )] \]

23911

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1] \]

23912

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )-x \left (t \right ) y \left (t \right )] \]

23913

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{2}, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+\left (x \left (t \right )^{2}-y \left (t \right )^{2}\right )^{5}] \]

23914

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right )+x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )+y \left (t \right )^{2}] \]

23915

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )] \]

23916

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )-x \left (t \right )^{2}+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -y \left (t \right )+2 x \left (t \right ) y \left (t \right )] \]

23917

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )] \]

23918

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )] \]

23919

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )] \]

23920

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )] \]

23921

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )] \]

23922

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )] \]

23923

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )] \]

23924

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]

23925

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )] \]

23926

\[ {} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

23927

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )] \]

23928

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )] \]

23929

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = -7 x \left (t \right )-9 y \left (t \right )] \]

23930

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )] \]

23931

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-x \left (t \right )^{2}+2 y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+x \left (t \right )^{2} y \left (t \right )^{2}] \]

23932

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}-x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )+x \left (t \right ) y \left (t \right )] \]

23933

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{2}] \]

23934

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 3 y \left (t \right )-x \left (t \right )^{2}] \]

23935

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )] \]

23936

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )] \]

23937

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )] \]

23938

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )] \]

23939

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right )] \]

23940

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )] \]

23941

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )] \]

23942

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )] \]

23943

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right )] \]

24048

\[ {} [y^{\prime }\left (x \right ) = -2, z^{\prime }\left (x \right ) = x \,{\mathrm e}^{y \left (x \right )+2 x}] \]

24049

\[ {} [y^{\prime }\left (x \right )+y \left (x \right ) = {\mathrm e}^{x}, z^{\prime }\left (x \right ) = y \left (x \right )] \]

24050

\[ {} [y^{\prime }\left (x \right ) = z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )] \]

24051

\[ {} [y \left (x \right ) y^{\prime }\left (x \right ) = -x, y \left (x \right ) z^{\prime }\left (x \right ) = 2] \]

24052

\[ {} [y^{\prime }\left (x \right )+2 z \left (x \right ) = y \left (x \right ), z^{\prime }\left (x \right )+4 y \left (x \right ) = 0] \]