4.24.16 Problems 1501 to 1600

Table 4.1383: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

8787

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

8809

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

8810

\[ {} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \]

8811

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

8812

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

8813

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

8814

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

8818

\[ {} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t} = 0 \]

8819

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

8821

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

8828

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

8831

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

8832

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

8837

\[ {} u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \]

8839

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

8843

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

8844

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

8845

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

8851

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

8960

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

8961

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

8962

\[ {} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \]

8963

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

8964

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

8965

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

8966

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

8967

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

8968

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

8969

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

8970

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

8971

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

8972

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

8981

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

8983

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

8984

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

8985

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

8986

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

8987

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

8988

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

8989

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

8990

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

8991

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

8992

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

8993

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

9046

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

9047

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

9049

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

9050

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

9051

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

9052

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

9053

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

9054

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

9110

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

9191

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

9192

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

9194

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

9195

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

9196

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

9197

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

9198

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

9199

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

9200

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

9201

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

9202

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

9219

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

9220

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

9221

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

9222

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

9247

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

9248

\[ {} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

9249

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

9250

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

9251

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

9252

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

9253

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

9254

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

9255

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

9286

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

9287

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

9288

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

9289

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

9290

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

9293

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

9294

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

9295

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

9296

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

9297

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

9298

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

9299

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

9300

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

9301

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

9321

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

9322

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

9323

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

9324

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

9347

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

9353

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

9357

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

9573

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]

9574

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