5.6.1 Problems 1 to 100

Table 5.547: Second order non-linear ODE

#

ODE

Mathematica

Maple

148

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

151

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

153

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

154

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

155

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

156

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

157

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

158

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

170

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

232

\[ {}y y^{\prime \prime } = 6 x^{4} \]

233

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

1360

\[ {}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \]

2820

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

2821

\[ {}z^{\prime \prime }+z+z^{5} = 0 \]

2822

\[ {}z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1 \]

2823

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

2824

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

3247

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

3248

\[ {}x^{\prime \prime } = \frac {k^{2}}{x^{2}} \]

3252

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

3256

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

3258

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

3259

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

3260

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

3261

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

3262

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

3263

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

3264

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

3265

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

3267

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

3268

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

3269

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

3270

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

3271

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

3273

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

3274

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

3275

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

3276

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

3277

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

3278

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

3279

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

3280

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

3281

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

3283

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

3483

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

3492

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

4407

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

4432

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

4436

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

5995

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

5996

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

5997

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

6000

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

6001

\[ {}r^{\prime \prime } = -\frac {k}{r^{2}} \]

6002

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

6003

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

6004

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

6005

\[ {}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \]

6006

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

6007

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

6008

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

6010

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

6011

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

6012

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

6013

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

6016

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

6017

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

6018

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

6030

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

6183

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

6184

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

6185

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

6186

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

6188

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

6189

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

6190

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

6191

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

6231

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

6235

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

6698

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

6699

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

6700

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

6772

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

6776

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

6777

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

6778

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

6781

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

6782

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

6786

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

6879

\[ {}u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right ) \]

6880

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

6881

\[ {}R^{\prime \prime } = -\frac {k}{R^{2}} \]

6882

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

6979

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

7006

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

7528

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

7533

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

7565

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

7761

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

7763

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