5.6.2 Problems 101 to 200

Table 5.549: Second order non-linear ODE

#

ODE

Mathematica

Maple

7765

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

7766

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

7767

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

7768

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

7824

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

7905

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

7906

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

7908

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

7909

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

7910

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

7912

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

7913

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

7914

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

7915

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

7916

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

7933

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

7934

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

7935

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

8071

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

8489

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

8490

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

8491

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

8492

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

8493

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

8494

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

8495

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

8498

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

8499

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

8501

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

8503

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

8504

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

8505

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

8506

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

8507

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

8508

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

8510

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

8511

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

8512

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

8513

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

8514

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

8515

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

8516

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

8517

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

8518

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

8519

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

8520

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

8521

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

8522

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

8523

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

8524

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

8525

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

8526

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

8527

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

8528

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

8774

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

8775

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

8776

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

8778

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

8779

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

8780

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

8781

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

8799

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

8803

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

8879

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

8880

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

8881

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

8882

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

8883

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

8884

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

8885

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

8962

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

8983

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

9084

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

9085

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

9087

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

9088

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

9090

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

9091

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

9093

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

9094

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

9116

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

9117

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

9118

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

9119

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

9120

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

9121

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

9122

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

9123

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

9124

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

9125

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

9126

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

9127

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

9128

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

9129

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

9131

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

9132

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

9133

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

9134

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

9135

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

9136

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