5.3.75 Problems 7401 to 7467

Table 5.195: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

25305

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

25308

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

25309

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25310

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]

25311

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25312

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25313

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25314

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25315

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

25316

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

25317

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

25318

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

25319

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

25320

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

25328

\[ {} y^{\prime \prime }-2 y^{\prime }-2 y = \frac {t^{2}+1}{-t^{2}+1} \]

25329

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

25330

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

25331

\[ {} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y = 0 \]

25332

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

25333

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]

25334

\[ {} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y = f \left (t \right ) \]

25335

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

25336

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

25353

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]

25354

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

25355

\[ {} t y^{\prime \prime }+\left (t +1\right ) y^{\prime }+y = 0 \]

25356

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

25358

\[ {} t y^{\prime \prime }-4 y^{\prime }+t y = 0 \]

25359

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

25360

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

25362

\[ {} t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y = 0 \]

25364

\[ {} t y^{\prime \prime \prime }+3 y^{\prime \prime }+t y^{\prime }+y = 0 \]

25365

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

25370

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

25373

\[ {} t y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+4 y = 0 \]

25374

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

25375

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

25376

\[ {} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y = 0 \]

25377

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

25378

\[ {} \left (1+\cos \left (2 t \right )\right ) y^{\prime \prime }-4 y = 0 \]

25381

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

25393

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}+1} \]

25394

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

25395

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

25396

\[ {} t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 4 t^{5} \]

25404

\[ {} -y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \]

25405

\[ {} 3 y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right . \]

25406

\[ {} -y+y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ -t +3 & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \]

25409

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right . \]

25411

\[ {} y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right . \]

25412

\[ {} y^{\prime }+5 y = \left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \]

25413

\[ {} y^{\prime }-3 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right . \]

25414

\[ {} y^{\prime }+2 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

25415

\[ {} y^{\prime }-4 y = \left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \]

25416

\[ {} 3 y+y^{\prime } = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

25418

\[ {} y^{\prime \prime }-5 y^{\prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right . \]

25419

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \]

25422

\[ {} y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \]

25452

\[ {} y^{\prime \prime }+\frac {\left (1-t \right ) y^{\prime }}{t}+\frac {\left (1-\cos \left (t \right )\right ) y}{t^{3}} = 0 \]

25454

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}} = 0 \]

25458

\[ {} t^{2} y^{\prime \prime }+t \,{\mathrm e}^{t} y^{\prime }+4 \left (1-4 t \right ) y = 0 \]

25475

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

25478

\[ {} [y_{1}^{\prime }\left (t \right ) = t \sin \left (y_{1} \left (t \right )\right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+t \cos \left (y_{2} \left (t \right )\right )] \]

25494

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

25498

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

25509

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

25510

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