4.24.37 Problems 3601 to 3700

Table 4.1083: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

18135

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

18142

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

18143

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

18154

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

18160

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

18165

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

18168

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

18170

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

18171

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

18173

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

18179

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

18181

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

18182

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \]

18184

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

18187

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

18191

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

18192

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

18195

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

18196

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

18197

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

18198

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

18199

\[ {} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0 \]

18200

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

18201

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

18202

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

18203

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

18204

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

18205

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

18206

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

18207

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

18208

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

18233

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

18234

\[ {} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

18235

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

18236

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

18237

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

18238

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

18239

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

18240

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

18241

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

18242

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

18243

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

18273

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

18274

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

18275

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

18276

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

18277

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

18297

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

18298

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

18299

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

18300

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

18335

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

18379

\[ {} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0 \]

18380

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

18381

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

18408

\[ {} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

18434

\[ {} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0 \]

18437

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

18452

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

18454

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

18455

\[ {} \cos \left (x \right ) y^{\prime }+y^{\prime \prime } \sin \left (x \right )+n y \sin \left (x \right ) = 0 \]

18457

\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

18459

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

18488

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

18489

\[ {} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

18511

\[ {} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6} \]

18512

\[ {} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right ) \]

18516

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

18517

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

18518

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

18519

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

18521

\[ {} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0 \]

18523

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

18526

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

18527

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x} \]

18529

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

18530

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

18531

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

18532

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

18533

\[ {} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0 \]

18534

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

18535

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

18536

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

18537

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

18538

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

18539

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

18605

\[ {} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2} \]

18606

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

18607

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

18608

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

18609

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

18610

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

18611

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

18612

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

18613

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

18614

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

18615

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

18616

\[ {} \left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right ) \]

18617

\[ {} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3} \]

18618

\[ {} x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}} \]