4.20.56 Problems 5501 to 5569

Table 4.1309: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

25251

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

25252

\[ {} y^{\prime \prime }+2 y^{\prime }-8 y = 6 \,{\mathrm e}^{-4 t} \]

25253

\[ {} y^{\prime \prime }+3 y^{\prime }-10 y = \sin \left (t \right ) \]

25254

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t} \]

25255

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = 10 t \,{\mathrm e}^{4 t} \]

25256

\[ {} y^{\prime \prime }-8 y^{\prime }+25 y = 36 t \,{\mathrm e}^{4 t} \sin \left (3 t \right ) \]

25257

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

25258

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

25259

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

25260

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

25263

\[ {} y^{\prime \prime \prime }-y = 0 \]

25264

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

25265

\[ {} y^{\prime \prime \prime \prime }-y = 0 \]

25266

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = 0 \]

25267

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \]

25268

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-25 y^{\prime }+50 y = 0 \]

25269

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }+25 y^{\prime }+50 y = 0 \]

25270

\[ {} y^{\left (6\right )}+27 y^{\prime \prime \prime \prime }+243 y^{\prime \prime }+729 y = 0 \]

25271

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+18 y^{\prime \prime }-27 y = 0 \]

25272

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

25273

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

25274

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

25275

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

25276

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

25277

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

25278

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

25279

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

25280

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

25281

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

25282

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

25297

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

25298

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

25328

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

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

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

25393

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

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

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

25437

\[ {} y^{\prime \prime }+9 y = 0 \]

25438

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

25439

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 0 \]

25440

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