4.26.27 Problems 2601 to 2700

Table 4.1543: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

18409

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

18422

\[ {} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

18423

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

18425

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

18426

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

18427

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

18482

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

18503

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0 \]

18504

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

18505

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0 \]

18506

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

18507

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

18508

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

18509

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

18510

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

18832

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

18834

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

18835

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

18847

\[ {} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 y \ln \left (t \right ) = 0 \]

18848

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

18849

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

18850

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

18852

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

18856

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

18857

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

18860

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]

18861

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

18862

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

18863

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

18864

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

18865

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

18866

\[ {} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \]

18867

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

18868

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

18869

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

18913

\[ {} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0 \]

18914

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

18915

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

18916

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

18917

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y = 0 \]

18918

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

18919

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

18920

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

18921

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

18922

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

18923

\[ {} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y = 0 \]

18924

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

18925

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

19281

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

19282

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

19283

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

19294

\[ {} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

19295

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

19312

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

19318

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

19319

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

19320

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

19321

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

19323

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

19507

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

19536

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

19544

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

19546

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

19547

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

19549

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

19552

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

19557

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

19560

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

19561

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

19562

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

19563

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

19564

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

19565

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

19566

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

19567

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

19568

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

19569

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

19570

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

19571

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

19572

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

19573

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

19598

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

19599

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

19600

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

19601

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

19602

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

19603

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

19604

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

19605

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

19606

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

19607

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

19608

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

19700

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

19744

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

19746

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

19799

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

19802

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

19819

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

19820

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

19888

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