4.24.47 Problems 4601 to 4700

Table 4.1445: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

19853

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

19854

\[ {} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

19876

\[ {} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6} \]

19877

\[ {} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right ) \]

19881

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

19882

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

19883

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

19884

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

19886

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

19888

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

19891

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

19892

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

19894

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

19895

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

19896

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

19897

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

19898

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

19899

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

19900

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

19901

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

19902

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

19903

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

19904

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

19969

\[ {} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2} \]

19970

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

19971

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

19972

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

19973

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

19974

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

19975

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

19976

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

19977

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

19978

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

19979

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

19980

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

19981

\[ {} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3} \]

19982

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

19984

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

19986

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

19987

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

19988

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

19989

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

19990

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

19994

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

19995

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

20009

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

20010

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

20208

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

20209

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

20210

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

20211

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

20212

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

20213

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

20214

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

20215

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

20216

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

20217

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

20218

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

20219

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

20220

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

20221

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

20222

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

20223

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

20224

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

20225

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

20226

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

20227

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

20228

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

20229

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

20230

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

20231

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

20232

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

20233

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

20234

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

20235

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

20236

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

20237

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

20238

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

20240

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

20243

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

20244

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

20245

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

20246

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

20247

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

20248

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

20249

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

20250

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

20251

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

20252

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

20253

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

20256

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

20257

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

20258

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

20259

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

20260

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

20267

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

20268

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

20269

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

20270

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

20272

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