4.26.29 Problems 2801 to 2900

Table 4.1547: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

20958

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

20959

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

20960

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

20974

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

20975

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

20976

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

20977

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

20978

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

20979

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

20980

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

20981

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

21118

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

21222

\[ {} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0 \]

21223

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x = 0 \]

21272

\[ {} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5} = 0 \]

21273

\[ {} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x = 0 \]

21274

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

21276

\[ {} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0 \]

21278

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

21279

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

21285

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

21286

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

21287

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

21290

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

21391

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

21392

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

21393

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

21394

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

21395

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

21575

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

21576

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

21590

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

21715

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

21717

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

21718

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

21720

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

21721

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

21727

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

21731

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \]

21732

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

21733

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

22080

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

22193

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

22197

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

22198

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

22431

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

22473

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

22602

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

22738

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

22754

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

22767

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

22768

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

22798

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

22799

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

22801

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

22868

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

22869

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

22875

\[ {} y^{\prime \prime } = \frac {\frac {4 x}{25}-\frac {4 y}{25}}{x^{2}} \]

22882

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

22883

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

22886

\[ {} \left (r^{2}+r \right ) R^{\prime \prime }+r R^{\prime }-n \left (n +1\right ) R = 0 \]

22887

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

22888

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

22890

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

22899

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

22913

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

22914

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

22917

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

22918

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

22933

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

23220

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

23355

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

23360

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

23366

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

23373

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

23390

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

23393

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

23394

\[ {} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0 \]

23395

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

23398

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

23400

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

23401

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

23402

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

23403

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

23404

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

23405

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

23411

\[ {} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \,{\mathrm e}^{x} = 0 \]

23412

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

23414

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

23416

\[ {} \left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1} = 0 \]

23484

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

23485

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

23486

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

23487

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

23488

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

23489

\[ {} \left (x -1\right )^{2} y^{\prime \prime }+5 \left (x -1\right ) y^{\prime }+4 y = 0 \]

23490

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

23491

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

23493

\[ {} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2} = 0 \]

23494

\[ {} \left (x +3\right )^{2} y^{\prime \prime }+3 \left (x +3\right ) y^{\prime }+5 y = 0 \]