4.24.38 Problems 3701 to 3800

Table 4.1085: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

18620

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

18622

\[ {} y^{\prime \prime } = \frac {1}{y^{2}} \]

18623

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

18624

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

18625

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

18626

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

18630

\[ {} V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0 \]

18631

\[ {} V^{\prime \prime }+\frac {V^{\prime }}{r} = 0 \]

18645

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

18646

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

18844

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

18845

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

18846

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

18847

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

18848

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

18849

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

18850

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2} \]

18851

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

18852

\[ {} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0 \]

18853

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

18854

\[ {} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

18855

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

18856

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

18857

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

18858

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

18859

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

18860

\[ {} 16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y = x^{2}+4 x +3 \]

18861

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

18862

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

18863

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2} \]

18864

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

18865

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

18866

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

18867

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

18868

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

18869

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

18870

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

18871

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

18872

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

18873

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

18874

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

18876

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

18879

\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]

18880

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

18881

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

18882

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

18883

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

18884

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

18885

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

18886

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

18887

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

18888

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

18889

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

18892

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

18893

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

18894

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

18895

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

18896

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

18903

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

18904

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

18905

\[ {} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (6 x +3\right ) y^{\prime \prime }+6 y = 0 \]

18906

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

18908

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

18909

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

18910

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

18911

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

18912

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

18913

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

18915

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

18918

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

18919

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

18921

\[ {} y^{3} y^{\prime \prime } = a \]

18923

\[ {} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2} \]

18924

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

18925

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

18926

\[ {} \left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

18927

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

18928

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

18929

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

18930

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

18931

\[ {} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

18932

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

18933

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

18934

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

18935

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

18936

\[ {} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5} \]

18937

\[ {} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

18938

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

18939

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

18940

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

18941

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

18942

\[ {} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0 \]

18943

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

18944

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

18945

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

18946

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

18947

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

18948

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

18949

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

18950

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