4.5.38 Problems 3701 to 3758

Table 4.723: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

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

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

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

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

25321

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25323

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25324

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25325

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25326

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25327

\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }-4 y = t^{4} \]

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

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

25332

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

25334

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

25382

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

25383

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

25384

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t} \]

25385

\[ {} y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{-3 t} \]

25386

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{3 t} \]

25387

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

25388

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

25389

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

25390

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

25391

\[ {} t y^{\prime \prime }-y^{\prime } = 3 t^{2}-1 \]

25392

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

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

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

25397

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

25398

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

25399

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

25400

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

25401

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

25402

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \]

25403

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

25408

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

25409

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

25417

\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -3\right ) \]

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

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

25420

\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]

25421

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

25422

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

25427

\[ {} y^{\prime \prime }+4 y = \delta \left (t -\pi \right ) \]

25428

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

25429

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

25430

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

25431

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 3 \delta \left (t -1\right ) \]

25432

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 3 \delta \left (t -\pi \right ) \]

25435

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

25436

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = \delta \left (t -3\right ) \]