5.7.16 Problems 1501 to 1600

Table 5.593: Solved using series method

#

ODE

Mathematica

Maple

13560

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

13561

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

13562

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

13563

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

13564

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

13565

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

13566

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

13567

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

13568

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

13569

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

13570

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

13571

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

13572

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

13573

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

13574

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

13575

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

13576

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

13577

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

13578

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

13579

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

13580

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

13581

\[ {}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0 \]

13582

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

13583

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

13584

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y = 0 \]

13585

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

13586

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

13587

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

13588

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

13589

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

13590

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

13591

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

13592

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

13593

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

13594

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

13595

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

13596

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

13597

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

13598

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

13599

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

13600

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

13601

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

13602

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

13603

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

13807

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

13808

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

13809

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

13810

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

13811

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

13812

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

13813

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

13814

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

13815

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

13816

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

13914

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

14138

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

14139

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

14140

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

14141

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

14142

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

14143

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

14144

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

14145

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

15647

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

15648

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

15649

\[ {}y^{\prime }+\frac {2 y}{2 x -1} = 0 \]

15650

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

15651

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

15652

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

15653

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

15654

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

15655

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

15656

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

15657

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

15658

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

15659

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

15660

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

15661

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

15662

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

15663

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

15664

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

15665

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

15666

\[ {}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0 \]

15667

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

15668

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

15669

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

15670

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

15671

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

15672

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

15673

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

15674

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

15675

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

15676

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

15677

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

15678

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

15679

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

15680

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

15681

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

15682

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

15683

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