4.24.45 Problems 4401 to 4500

Table 4.1441: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

18510

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

18832

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

18833

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

18834

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

18835

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

18836

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

18837

\[ {} y^{\prime \prime }-t y = \frac {1}{\pi } \]

18838

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

18844

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

18845

\[ {} \left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right ) \]

18846

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

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

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

18851

\[ {} y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi } \]

18852

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

18853

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

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

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

18958

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

18959

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

18960

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

18961

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

18971

\[ {} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

18972

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

18985

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

18986

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

18987

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

18988

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

18989

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

18990

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

18991

\[ {} t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

18992

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

18993

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

18994

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

18996

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

18997

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

19081

\[ {} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right ) \]

19082

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

19083

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

19084

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

19085

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

19087

\[ {} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right ) \]

19088

\[ {} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0 \]

19089

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

19090

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

19091

\[ {} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0 \]

19098

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

19099

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

19257

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

19258

\[ {} a^{3} y^{\prime \prime \prime } y^{\prime \prime } = \sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \]

19259

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

19260

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

19261

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

19262

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

19263

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

19264

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

19265

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

19266

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

19267

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

19268

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

19269

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

19270

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

19271

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

19272

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

19273

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

19274

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

19275

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

19276

\[ {} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0 \]

19277

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

19278

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

19279

\[ {} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y = 0 \]

19280

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

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

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