3.10.6 Problems 501 to 600

Table 3.637: System of differential equations

#

ODE

Mathematica

Maple

11568

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+3, y^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )+2 t] \]

11569

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

11928

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

11929

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

11930

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

11931

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

11932

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

11933

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

11934

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

11935

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

11936

\[ {}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0] \]

11937

\[ {}[x^{\prime }\left (t \right )-y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 1] \]

11938

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

11939

\[ {}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )+5 y \left (t \right ) = t^{2}, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = 2 t +1] \]

11940

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

11941

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

11942

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

11943

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

11944

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

11945

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

11946

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

11947

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )+5 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )+17 t] \]

11948

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

11949

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

11950

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

11951

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )] \]

11966

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

11967

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

12081

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

12082

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

12083

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

12084

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

12085

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

12086

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

12087

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )] \]

12097

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )] \]

12098

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

12099

\[ {}[x^{\prime }\left (t \right ) = 11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )] \]

12100

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+20 y \left (t \right ), y^{\prime }\left (t \right ) = 40 x \left (t \right )-19 y \left (t \right )] \]

12101

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

12102

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

12103

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )+4 y \left (t \right )] \]

12104

\[ {}[x^{\prime }\left (t \right ) = -11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 13 x \left (t \right )-9 y \left (t \right )] \]

12105

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 10 x \left (t \right )-3 y \left (t \right )] \]

12106

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

12107

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

12108

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

12109

\[ {}[x^{\prime }\left (t \right ) = 13 x \left (t \right ), y^{\prime }\left (t \right ) = 13 y \left (t \right )] \]

12110

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )] \]

12111

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

12208

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

12209

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

12210

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

12211

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

12362

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

12363

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

12364

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

12365

\[ {}[x^{\prime }\left (t \right )+5 x \left (t \right )-2 y \left (t \right ) = 0, y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = 0] \]

12366

\[ {}[x^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right ) = 0, y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = 0] \]

12367

\[ {}[x^{\prime }\left (t \right )+x \left (t \right )-z \left (t \right ) = 0, y^{\prime }\left (t \right )-y \left (t \right )+x \left (t \right ) = 0, z^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ) = 0] \]

12368

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

12369

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

12370

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

12371

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

12372

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

12373

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

12374

\[ {}[x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right ) = 0, 2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right ) = t +y \left (t \right )] \]

12375

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

12376

\[ {}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+9 y \left (t \right )+12 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = -5 x \left (t \right )+2 y \left (t \right )] \]

12377

\[ {}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+6 y \left (t \right )+6 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = -12 x \left (t \right )+5 y \left (t \right )+37] \]

12378

\[ {}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+10 y \left (t \right )+18 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -10 x \left (t \right )+9 y \left (t \right )+37] \]

12379

\[ {}[x^{\prime }\left (t \right ) = -14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right )] \]

12380

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right )-2 \sinh \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+10 \cosh \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5] \]

12381

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )-2 z \left (t \right )+50 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 6 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+21 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = -x \left (t \right )+6 y \left (t \right )+z \left (t \right )+9] \]

12382

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t}] \]

12383

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

12384

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )-1-6 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )+4 \,{\mathrm e}^{t}-3] \]

12385

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+24 \sin \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )+12 \cos \left (t \right )] \]

12386

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right )+10 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 3 x \left (t \right )+14 y \left (t \right )+6 \,{\mathrm e}^{2 t}] \]

12387

\[ {}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = -5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t}] \]

12388

\[ {}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t}] \]

12389

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )+5 \sin \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right )-10 \cos \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right )+2] \]

12390

\[ {}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \sin \left (2 t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right )-3 z \left (t \right )+5 \cos \left (2 t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )+7 y \left (t \right )+3 z \left (t \right )+23 \,{\mathrm e}^{t}] \]

12391

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

12392

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right ), y^{\prime }\left (t \right ) = 19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right )] \]

12393

\[ {}[x^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )-6 t, y^{\prime }\left (t \right ) = -x \left (t \right )+11 y \left (t \right )+10 t] \]

12536

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

12537

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

12538

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

12549

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+6 y \left (t \right )] \]

12550

\[ {}[x^{\prime }\left (t \right ) = -4 x \left (t \right )-10 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )] \]

12551

\[ {}[x^{\prime }\left (t \right ) = 12 x \left (t \right )+18 y \left (t \right ), y^{\prime }\left (t \right ) = -8 x \left (t \right )-12 y \left (t \right )] \]

12554

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

12555

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

12556

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

12557

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

12558

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

12559

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

12560

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

12561

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