4.3.63 Problems 6201 to 6300

Table 4.409: Second order ode

#

ODE

Mathematica

Maple

Sympy

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

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

18949

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

18950

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

18951

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

18952

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

18953

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

18954

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

18955

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

18956

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

18966

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

18967

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

19080

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

19082

\[ {} 2 x^{\prime \prime }+5 x^{\prime }-12 x = 0 \]

19083

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

19084

\[ {} 9 x^{\prime \prime }+18 x^{\prime }-16 x = 0 \]

19086

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

19094

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

19095

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

19096

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2} \]

19097

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

19098

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}} \]

19099

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

19100

\[ {} y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x} \]

19101

\[ {} y^{\prime \prime }+9 y = \sin \left (2 x \right )+\cos \left (2 x \right ) \]

19102

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

19103

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

19105

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

19106

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

19112

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

19113

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

19114

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

19117

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x} \]

19118

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

19121

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

19122

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

19123

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

19127

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

19130

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0 \]

19236

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

19237

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

19244

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

19246

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

19247

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

19248

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

19249

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

19250

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

19251

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

19252

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

19253

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

19254

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

19255

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

19259

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

19262

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

19263

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

19266

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

19267

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

19268

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

19269

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

19270

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

19273

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

19274

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

19275

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

19276

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

19277

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

19278

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

19279

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

19280

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

19284

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

19287

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

19288

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

19289

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

19291

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

19293

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

19294

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

19295

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

19296

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

19297

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

19298

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

19299

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

19300

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

19301

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

19302

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

19303

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

19304

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

19306

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

19307

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

19308

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

19309

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

19311

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

19312

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

19313

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

19314

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

19315

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

19316

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

19317

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

19318

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