4.10.15 Problems 1401 to 1500

Table 4.1045: System of differential equations

#

ODE

Mathematica

Maple

Sympy

20324

\[ {} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}] \]

20325

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

20326

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

20327

\[ {} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right ) = 3] \]

20328

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

20329

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

20792

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

20923

\[ {} [x^{\prime }\left (t \right )-7 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right ) = 0] \]

20924

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

20925

\[ {} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right ) = {\mathrm e}^{2 t}] \]

20926

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

21037

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

21038

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

21039

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

21040

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

21041

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

21042

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

21043

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

21044

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

21045

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

21046

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

21047

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

21048

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

21049

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

21050

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

21051

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

21052

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

21053

\[ {} [x^{\prime }\left (t \right ) = 12 x \left (t \right )-15 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )] \]

21054

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

21055

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right )] \]

21056

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

21057

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

21058

\[ {} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 16 x \left (t \right )+8 y \left (t \right )] \]

21059

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

21060

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

21061

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

21062

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right )+1, y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{t}] \]

21063

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

21107

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

21108

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

21109

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

21110

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

21111

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

21112

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

21113

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

21117

\[ {} \left [w_{1}^{\prime }\left (z \right ) = w_{2} \left (z \right ), w_{2}^{\prime }\left (z \right ) = \frac {a w_{1} \left (z \right )}{z^{2}}\right ] \]

21218

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

21219

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

21320

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

21321

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

21322

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

21323

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

21324

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

21325

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

21326

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

21327

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

21328

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

21329

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

21330

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

21331

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

21332

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

21333

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

21334

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

21335

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

21336

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

21337

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

21338

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

21339

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

21340

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

21341

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

21342

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

21343

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

21344

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

21345

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

21346

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

21348

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

21349

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

21350

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

21351

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

21352

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

21353

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

21354

\[ {} [t^{2} x^{\prime }\left (t \right )-y \left (t \right ) = 1, y^{\prime }\left (t \right )-2 x \left (t \right ) = 0] \]

21355

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

21356

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

21357

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

21358

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

21359

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

21360

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

21361

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

21362

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

21363

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

21365

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

21366

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

21367

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

21368

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

21369

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

21406

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

21407

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

21408

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

21409

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