4.6.5 Problems 401 to 500

Table 4.733: Second order non-linear ODE

#

ODE

Mathematica

Maple

Sympy

8851

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

9047

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

9049

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

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

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

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

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

9357

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

9775

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

9776

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

9777

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

9778

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

9779

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

9780

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

9781

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

9784

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

9785

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

9787

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

9789

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

9790

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

9791

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

9792

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

9793

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

9794

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

9796

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

9797

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

9798

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

9799

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

9800

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

9801

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

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

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

9809

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

9810

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

9811

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

9812

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

9813

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

9814

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

10060

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

10061

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

10062

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

10064

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

10065

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

10066

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

10067

\[ {} a y^{2} y^{\prime \prime }+b y^{2} = c \]

10085

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

10089

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

10165

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

10166

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

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

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

10248

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

10269

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

10384

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

10385

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

10387

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

10388

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

10390

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

10391

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

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

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