4.5.5 Problems 401 to 500

Table 4.657: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

3190

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

3205

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

3206

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

3207

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

3210

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

3214

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

3215

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

3216

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

3217

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

3218

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

3219

\[ {} y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

3220

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

3225

\[ {} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right ) \]

3226

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

3227

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

3228

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

3230

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

3231

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

3232

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

3244

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

3247

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

3249

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

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

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

3261

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

3265

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

3269

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

3272

\[ {} y^{\prime \prime } = \tan \left (x \right ) \sec \left (x \right ) \]

3277

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

3484

\[ {} x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \]

3486

\[ {} f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

3487

\[ {} f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \]

3488

\[ {} f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

3489

\[ {} f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

3490

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

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

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

3496

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

3497

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

3500

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

3568

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

3569

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

3584

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

3585

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

3587

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

3589

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

3592

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

3631

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

3711

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \]

3712

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

3716

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

3717

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

3718

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

3719

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \]

3720

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

3724

\[ {} y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \]

3725

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

3726

\[ {} y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right ) \]

3727

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

3728

\[ {} y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \]

3729

\[ {} y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \]

3732

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

3733

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

3734

\[ {} y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \]

3735

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 50 \sin \left (3 x \right ) \]

3736

\[ {} -y+y^{\prime \prime } = 10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

3737

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \]

3738

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2} \]

3739

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

3740

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

3741

\[ {} y^{\prime \prime }-4 y = 100 \,{\mathrm e}^{x} \sin \left (x \right ) x \]

3742

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \]

3743

\[ {} y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \]

3744

\[ {} y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \]

3745

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \]

3746

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

3747

\[ {} y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3} \]

3748

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \]

3749

\[ {} y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \]

3750

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right ) \]

3751

\[ {} y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}} \]

3752

\[ {} y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \]

3753

\[ {} y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \]

3754

\[ {} y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x} \]

3755

\[ {} y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1 \]

3756

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

3757

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

3758

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

3759

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

3760

\[ {} y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \]

3761

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

3762

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \]

3767

\[ {} y^{\prime \prime }-9 y = F \left (x \right ) \]

3768

\[ {} y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right ) \]

3769

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

3770

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right ) \]