3.14.10 Problems 901 to 943

Table 3.699: First order ode non-linear in derivative

#

ODE

Mathematica

Maple

15093

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

15094

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

15095

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

15096

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

15097

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

15098

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

15099

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

15100

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

15101

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

15102

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

15103

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

15104

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

15105

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

15106

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

15107

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

15108

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

15109

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

15110

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

15111

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

15112

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

15113

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

15114

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

15115

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

15116

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

15117

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

15122

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

15123

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

15124

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

15125

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

15127

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

15128

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

15129

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

15130

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

15131

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

15132

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

15133

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

15134

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

15135

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

15136

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

15174

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

15175

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

15180

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

15195

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