4.20.25 Problems 2401 to 2500

Table 4.1247: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

15061

\[ {} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \]

15062

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

15063

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

15064

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

15071

\[ {} y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x} \]

15072

\[ {} x^{\prime \prime }-x = \frac {1}{t} \]

15073

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

15075

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

15087

\[ {} a y^{\prime \prime }+\left (-a +b \right ) y^{\prime }+c y = 0 \]

15181

\[ {} y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

15182

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

15183

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

15184

\[ {} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}} \]

15186

\[ {} y^{\prime \prime }+y = \cosh \left (x \right ) \]

15188

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

15191

\[ {} y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

15193

\[ {} x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \]

15194

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

15199

\[ {} y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )} \]

15203

\[ {} x^{\prime \prime }+9 x = t \sin \left (3 t \right ) \]

15204

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

15205

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

15206

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

15210

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

15211

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

15214

\[ {} x^{\prime \prime \prime \prime }+x = t^{3} \]

15215

\[ {} {y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x \]

15216

\[ {} x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

15218

\[ {} y^{\left (6\right )}-y = {\mathrm e}^{2 x} \]

15219

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

15222

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

15242

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

15252

\[ {} y^{\prime \prime \prime } = 1 \]

15254

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

15261

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

15262

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

15263

\[ {} 2 y^{\prime \prime }-3 y^{\prime }-2 y = 0 \]

15264

\[ {} 3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 0 \]

15300

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

15301

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

15302

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

15303

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

15304

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

15305

\[ {} 4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]

15306

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]

15307

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

15308

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]

15309

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

15310

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

15311

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

15312

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

15313

\[ {} y^{\prime \prime }-20 y^{\prime }+51 y = 0 \]

15314

\[ {} 2 y^{\prime \prime }+3 y^{\prime }+y = 0 \]

15315

\[ {} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \]

15316

\[ {} 2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

15317

\[ {} 4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]

15318

\[ {} y^{\prime \prime }+6 y^{\prime }+34 y = 0 \]

15319

\[ {} y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime } = 0 \]

15320

\[ {} y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime } = 0 \]

15321

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime } = 0 \]

15322

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0 \]

15323

\[ {} y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0 \]

15324

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0 \]

15325

\[ {} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]

15326

\[ {} y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \]

15327

\[ {} 4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \]

15328

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

15329

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

15330

\[ {} y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \]

15331

\[ {} 2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \]

15332

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

15333

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

15335

\[ {} y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \]

15336

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

15337

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

15339

\[ {} 3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \]

15342

\[ {} y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]

15343

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

15344

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

15345

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \]

15346

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \]

15347

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

15348

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

15349

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \]

15350

\[ {} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]

15351

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

15352

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

15353

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

15354

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

15355

\[ {} y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \]

15356

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

15357

\[ {} y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \]

15358

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

15359

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

15360

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right ) \]

15362

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8 \]

15363

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

15364

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \]

15365

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10 \]

15366

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right ) \]