4.14.10 Problems 901 to 1000

Table 4.1141: First order ode non-linear in derivative

#

ODE

Mathematica

Maple

Sympy

17449

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

17451

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

17452

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

18009

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

18010

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

18011

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

18012

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

18013

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

18014

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

18015

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

18104

\[ {} 4 {y^{\prime }}^{2}-9 x = 0 \]

18105

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

18106

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

18107

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

18108

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

18109

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

18110

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

18111

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

18112

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

18113

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

18114

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

18115

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

18116

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

18117

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

18118

\[ {} y = \left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \]

18119

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

18120

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

18121

\[ {} y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}} = a^{{2}/{5}} \]

18122

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

18123

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

18124

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

18125

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

18126

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

18127

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

18128

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

18129

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

18130

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

18131

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

18132

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

18133

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

18134

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

18139

\[ {} y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x = 0 \]

18140

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

18141

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

18142

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

18144

\[ {} \left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (-2 y+x y^{\prime }\right ) = 0 \]

18145

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

18146

\[ {} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \]

18147

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

18148

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

18149

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

18150

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

18151

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

18152

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

18153

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

18191

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

18192

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

18197

\[ {} {y^{\prime }}^{4} = 1 \]

18212

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

19222

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

19223

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

19224

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

19225

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

19226

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

19227

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

19228

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

19229

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

19230

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

19231

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

19232

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

19233

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

19234

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

19235

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

19236

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

19237

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

19238

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

19239

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

19240

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

19248

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

19249

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

19250

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

19251

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

19252

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

19253

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

19254

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

19255

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

19352

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

19845

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

19846

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

19847

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

19849

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

19859

\[ {} \sqrt {1+v^{\prime }} = \frac {{\mathrm e}^{u}}{2} \]

19865

\[ {} 4 {y^{\prime }}^{3} y-2 x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +x^{3} = 16 y^{2} \]

19887

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

19889

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

19992

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

19993

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

20008

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

20086

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

20087

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