4.18.3 Problems 201 to 254

Table 4.1177: Second order, non-linear and non-homogeneous

#

ODE

Mathematica

Maple

Sympy

19477

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

19483

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

19484

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

19508

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

19886

\[ {} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0 \]

19988

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

19989

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

20248

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

20251

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

20257

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

20285

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

20287

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

20293

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

20319

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

20660

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

20679

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

20683

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

20686

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

20688

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

20690

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

20691

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

20692

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

20882

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

20890

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

21440

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

21676

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

21681

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

21728

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

21729

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

21873

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

21877

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

21881

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

21905

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

22067

\[ {} s^{2} t^{\prime \prime }+s t t^{\prime } = s \]

22069

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

22075

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

22204

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

22441

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

22472

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

22600

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

22605

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

22613

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

23164

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

23354

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

23408

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

24038

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

24041

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

25010

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

25019

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

25020

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

25023

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

25024

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

25203

\[ {} y^{\prime \prime }-y y^{\prime } = 6 \]

25301

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