4.4.17 Problems 1601 to 1700

Table 4.577: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

9802

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

9803

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

9804

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

9805

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

9806

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

9807

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

9808

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

9811

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

9812

\[ {} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

9892

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

9893

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

9894

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

9895

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

9896

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

9897

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

9898

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

9899

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

9900

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

9912

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

9943

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

10038

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

10039

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

10046

\[ {} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \]

10047

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

10048

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

10049

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

10050

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

10051

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

10052

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

10059

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

10063

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

10068

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

10085

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

10086

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

10087

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

10088

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

10145

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

10167

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

10168

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

10169

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

10170

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

10171

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

10240

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

10242

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

10243

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

10247

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

10248

\[ {} y^{\prime \prime } = A y^{{2}/{3}} \]

10249

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

10250

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

10251

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

10267

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

10269

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

10372

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

10373

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

10374

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

10375

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

10376

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

10377

\[ {} a {y^{\prime \prime }}^{n} = 0 \]

10382

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

10383

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

10384

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

10385

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

10392

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

10393

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

10394

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

10416

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

10417

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

10418

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

10419

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

10420

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

10421

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

10422

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

10423

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

10424

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

10425

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

10426

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

10427

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

10428

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

10429

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

10431

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

10432

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

10433

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

10434

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

10435

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

10436

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

10439

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

10440

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

10443

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

10445

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

10451

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

10452

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

10457

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

10458

\[ {} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

10459

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

10460

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

10461

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

10468

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

10469

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

10473

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

10474

\[ {} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]