4.7.16 Problems 1501 to 1600

Table 4.779: Solved using series method

#

ODE

Mathematica

Maple

Sympy

10360

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

10361

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

10362

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

10363

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

10364

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

10365

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

10366

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

10367

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

10368

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

10369

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

10370

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

10371

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

10466

\[ {} x^{2} y^{\prime \prime }-x \left (x +6\right ) y^{\prime }+10 y = 0 \]

10467

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

14841

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

14842

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

14843

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

14844

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

14845

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

14846

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

14847

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

14848

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

14849

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

14850

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

14851

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

14852

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

14853

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

14854

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

14855

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

14856

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

14857

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

14858

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

14859

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

14860

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

14861

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

14862

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

14863

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

14864

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

14865

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

14866

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

14867

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

14868

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

14869

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

14870

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

14871

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

14872

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

14873

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

14874

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

14875

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

14876

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

14877

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

14878

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

14879

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

14880

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

14881

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

14882

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

14883

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

14884

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

15088

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

15089

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

15090

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

15091

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

15092

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

15093

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

15094

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

15095

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

15096

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

15097

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

15195

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

15419

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

15420

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

15421

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

15422

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

15423

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

15424

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

15425

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

15426

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

16934

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

16935

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

16936

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

16937

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

16938

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

16939

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

16940

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

16941

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

16942

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

16943

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

16944

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

16945

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

16946

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

16947

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

16948

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

16949

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

16950

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

16951

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

16952

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

16953

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

16954

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

16955

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

16956

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