4.24.4 Problems 301 to 400

Table 4.1359: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

3232

\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (x -1\right ) \ln \left (x \right ) \]

3233

\[ {} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right ) \]

3234

\[ {} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y = \frac {4}{x^{2}} \]

3235

\[ {} x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y = \cos \left (\ln \left (x \right )\right ) \]

3236

\[ {} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right ) \]

3247

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

3248

\[ {} x^{\prime \prime } = \frac {k^{2}}{x^{2}} \]

3249

\[ {} x y^{\prime \prime } = x^{2}+1 \]

3250

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

3251

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

3252

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

3253

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

3254

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

3255

\[ {} x^{2} y^{\prime \prime } = x y^{\prime }+1 \]

3256

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

3257

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

3258

\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]

3259

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

3260

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

3261

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

3262

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

3263

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

3264

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

3265

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

3267

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

3268

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

3269

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

3270

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

3271

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

3273

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

3274

\[ {} y^{\prime \prime } = y^{3} \]

3275

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

3276

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

3277

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

3278

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

3279

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

3280

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

3281

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

3283

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

3284

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

3483

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

3492

\[ {} \frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y} = 2 a^{2} \]

3493

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

3494

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

3495

\[ {} \left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0 \]

3498

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

3499

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

3500

\[ {} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \]

3565

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

3566

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

3567

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

3568

\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \]

3569

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

3575

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

3576

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

3591

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0 \]

3592

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

3631

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x \]

3707

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

3708

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

3709

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

3710

\[ {} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime } = 0 \]

3773

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

3774

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

3775

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right ) \]

3776

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2} \]

3777

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

3778

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

3779

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )} \]

3780

\[ {} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k} \]

3781

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

3782

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

3783

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

3784

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

3785

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

3786

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

3787

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0 \]

3788

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

3790

\[ {} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x} \]

3791

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4} \]

3794

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

3805

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

4139

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

4140

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

4165

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

4407

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

4414

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

4426

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

4432

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

4436

\[ {} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0 \]

4509

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

4510

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

4511

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \ln \left (x \right ) \]

4512

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

4513

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

5747

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

5748

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

5749

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

5750

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

5751

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