4.6.10 Problems 901 to 1000

Table 4.743: Second order non-linear ODE

#

ODE

Mathematica

Maple

Sympy

19896

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

19897

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

19899

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

19986

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

19987

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

19988

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

19989

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

20237

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

20238

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

20243

\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]

20244

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

20245

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

20247

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

20248

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

20250

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

20251

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

20252

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

20253

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

20257

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

20258

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

20267

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

20272

\[ {} {y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \]

20274

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

20279

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

20285

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

20287

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

20293

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

20318

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

20319

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

20642

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

20660

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

20662

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

20663

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

20664

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

20666

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

20673

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

20678

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

20679

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

20680

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

20681

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

20682

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

20683

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

20684

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

20686

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

20688

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

20689

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

20690

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

20691

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

20692

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

20699

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

20700

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

20701

\[ {} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \]

20702

\[ {} x^{4} y^{\prime \prime } = \left (x^{3}+2 x y\right ) y^{\prime }-4 y^{2} \]

20703

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

20704

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

20705

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

20710

\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]

20712

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

20713

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

20717

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

20765

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

20874

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

20882

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

20883

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

20884

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

20885

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

20889

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

20890

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

20891

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

20892

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

20893

\[ {} y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \]

20896

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

20897

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

21280

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

21281

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

21282

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

21283

\[ {} x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2} = 0 \]

21284

\[ {} x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2} = 0 \]

21364

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

21370

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

21371

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

21372

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

21373

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

21374

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

21375

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

21376

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

21377

\[ {} x^{\prime \prime }+x+8 x^{7} = 0 \]

21378

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

21379

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

21380

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

21381

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

21382

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

21434

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

21435

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

21436

\[ {} x^{\prime \prime }+6 x^{5} = 0 \]

21437

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

21438

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

21439

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

21440

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

21441

\[ {} -x^{\prime \prime }+x = {\mathrm e}^{-x} \]