4.29.8 Problems 701 to 800

Table 4.1625: Second order, Linear, non-homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

21672

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

21673

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

21675

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

21680

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

21716

\[ {} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y = x^{3}-3 x^{2}+3 x -8 \]

21725

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

21730

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 1 \]

22052

\[ {} x y^{\prime \prime }+y^{\prime } = 16 x^{3} \]

22066

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

22072

\[ {} t^{2} s^{\prime \prime }-t s^{\prime } = 1-\sin \left (t \right ) \]

22271

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

22272

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

22418

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

22575

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

22598

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

22607

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

22690

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

22706

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{r} = 4-4 r \]

22732

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

22736

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

22743

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

22769

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

22854

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

22870

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

22871

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

22872

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{2}+16 \ln \left (x \right )^{2} \]

22873

\[ {} x^{2} y^{\prime \prime }+y = 16 \sin \left (\ln \left (x \right )\right ) \]

22874

\[ {} t^{2} i^{\prime \prime }+2 i^{\prime } t +i = t \ln \left (t \right ) \]

22876

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = \sqrt {x}+\frac {1}{\sqrt {x}} \]

22877

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

22881

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

22884

\[ {} \left (2 x +3\right )^{2} y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }-2 y = 24 x^{2} \]

22885

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

22889

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

22891

\[ {} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1}{x^{2}} \]

22906

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 24+24 x \]

23197

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

23217

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

23221

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

23225

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

23346

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

23363

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

23365

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

23406

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

23410

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

23413

\[ {} 2 x y^{\prime \prime }-7 \cos \left (x \right ) y^{\prime }+y = {\mathrm e}^{-x} \]

23415

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

23577

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

23581

\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }-10 y = x \ln \left (x \right ) \]

23582

\[ {} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-8 y = 5+3 x \]

23584

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

23618

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

23619

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

23654

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

23655

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

23656

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

23657

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

23658

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \]

23666

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

23667

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

23669

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

23877

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

23962

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

24037

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

24039

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

24042

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

24125

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

24126

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

24127

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

24128

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

24157

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

24158

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

24177

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

24193

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

24992

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

24993

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

25005

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

25300

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

25302

\[ {} y^{\prime \prime }+\sqrt {t}\, y^{\prime }+y = \sqrt {t} \]

25307

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

25308

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

25309

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25311

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25312

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25313

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25314

\[ {} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t \]

25315

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

25317

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

25318

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

25319

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

25320

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

25321

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25323

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25324

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25325

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25326

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = t^{5} \]

25327

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

25329

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

25330

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

25332

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