4.24.31 Problems 3001 to 3100

Table 4.1071: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

13912

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

13913

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

13914

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

13915

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

13916

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

13917

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

13918

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

13919

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

13920

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

13921

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

13922

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

13923

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

13924

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

13925

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

13926

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

13927

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

13928

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

13929

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

13930

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

13931

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

13932

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

13933

\[ {} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

13934

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

13935

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \]

13936

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

13937

\[ {} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y = 0 \]

13938

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

13939

\[ {} y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

14008

\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

14009

\[ {} t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right ) \]

14010

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

14011

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

14012

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

14051

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

14052

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

14055

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

14057

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

14058

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

14067

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

14068

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

14069

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

14073

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

14074

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

14079

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

14081

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

14082

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

14147

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

14148

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

14150

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

14151

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

14152

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

14153

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

14154

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

14155

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

14156

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

14157

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

14196

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

14225

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

14226

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

14227

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

14228

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

14229

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

14231

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

14233

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

14235

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

14241

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

14248

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

14249

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

14250

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

14265

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

14266

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

14267

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

14268

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

14269

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

14270

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

14271

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

14402

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

14403

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

14404

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

14405

\[ {} \sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

14406

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

14409

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

14410

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

14413

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

14416

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

14906

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

14907

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

14909

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

14928

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

15130

\[ {} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

15131

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

15134

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

15135

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

15136

\[ {} y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \]

15137

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

15138

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

15139

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

15140

\[ {} x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5} \]

15141

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

15143

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