4.7.15 Problems 1401 to 1500

Table 4.777: Solved using series method

#

ODE

Mathematica

Maple

Sympy

9955

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

9956

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

9957

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

9958

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

9959

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

9960

\[ {} 2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime } = 0 \]

9961

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

9962

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0 \]

9963

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

9964

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

9965

\[ {} 4 x y-\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]

9966

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

9967

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

9968

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

9969

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

9970

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

9971

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

9972

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

9973

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

9974

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

9975

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

9976

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

9977

\[ {} x \left (-x^{2}+1\right ) y^{\prime \prime }+5 y^{\prime } \left (-x^{2}+1\right )-4 x y = 0 \]

9978

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

9979

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

9980

\[ {} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y = 0 \]

9981

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

9982

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

10176

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

10177

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

10178

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

10179

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

10180

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

10181

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

10182

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

10183

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

10184

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

10185

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

10186

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

10187

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

10188

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

10189

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

10190

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

10191

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

10192

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

10193

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

10194

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

10195

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

10196

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

10197

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

10198

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

10199

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

10200

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

10201

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

10202

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

10203

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

10204

\[ {} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

10205

\[ {} x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (1+x \right ) y^{\prime }-\left (1-4 x \right ) y = 0 \]

10206

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

10209

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

10210

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

10211

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

10212

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

10213

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

10214

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

10215

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

10216

\[ {} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \]

10217

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

10218

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

10219

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

10220

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

10221

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

10222

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

10223

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

10224

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

10225

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

10226

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

10227

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

10228

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

10229

\[ {} x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0 \]

10230

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

10231

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

10232

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

10233

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

10234

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

10235

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

10236

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

10237

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

10244

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

10254

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

10255

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

10256

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

10257

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

10258

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

10259

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

10260

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

10261

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

10265

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

10358

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

10359

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