4.14.9 Problems 801 to 900

Table 4.1139: First order ode non-linear in derivative

#

ODE

Mathematica

Maple

Sympy

11862

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

11863

\[ {} a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+b x y^{\prime }-y = 0 \]

11864

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

11865

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

11866

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

11867

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

11868

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

11869

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

11870

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

11871

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

11872

\[ {} a \,x^{n} f \left (y^{\prime }\right )+x y^{\prime }-y = 0 \]

11873

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

11874

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

14157

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

14158

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

14159

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

14160

\[ {} \left (2 x y^{\prime }-y\right )^{2} = 8 x^{3} \]

14161

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

14162

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

14163

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

14164

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

14165

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

14167

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

14168

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

14169

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

14170

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

14171

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

14172

\[ {} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0 \]

14173

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

14174

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0 \]

14175

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0 \]

14176

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

14177

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

14178

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

14179

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

14180

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

14181

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

14182

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

14183

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

14184

\[ {} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0 \]

14185

\[ {} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0 \]

14186

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

14187

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

14188

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

14189

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

14190

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

14191

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

14192

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

14193

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

14194

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

14195

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

14196

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

14197

\[ {} 8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \]

14198

\[ {} 4 {y^{\prime }}^{2} = 9 x \]

14199

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

14361

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

14541

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

15139

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

15140

\[ {} {y^{\prime }}^{2} = 9 y^{4} \]

15142

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

15144

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

15146

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

15147

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

15154

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

15155

\[ {} y = 5 x y^{\prime }-{y^{\prime }}^{2} \]

15161

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

15162

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

15165

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

15167

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

15178

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

15179

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

15180

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

15248

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

15250

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

15256

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

15442

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

15443

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

15444

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

15476

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

15502

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

15503

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

15504

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

15505

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

15506

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

15507

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

15509

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

15510

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

15564

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

15617

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

15618

\[ {} {y^{\prime }}^{2}-9 x y = 0 \]

15619

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

17071

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

17412

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

17413

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

17414

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

17415

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

17416

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

17417

\[ {} y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \]

17418

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

17420

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