3.14.2 Problems 101 to 200

Table 3.683: First order ode non-linear in derivative

#

ODE

Mathematica

Maple

4019

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

4020

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

4021

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

4022

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

4023

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

4024

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

4025

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

4026

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

4027

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

4028

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

4029

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

4030

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

4031

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

4032

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

4033

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

4034

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

4035

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

4036

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

4037

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

4038

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

4039

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

4040

\[ {}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0 \]

4041

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

4042

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

4043

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

4044

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

4045

\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \]

4046

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

4047

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

4048

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

4049

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

4050

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

4051

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

4052

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

4053

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

4054

\[ {}{y^{\prime }}^{2}-2 \left (-3 y+1\right ) y^{\prime }-\left (4-9 y\right ) y = 0 \]

4055

\[ {}{y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right ) = 0 \]

4056

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

4057

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

4058

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

4059

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

4060

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

4061

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

4062

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

4063

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

4064

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

4065

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

4066

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

4067

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

4068

\[ {}{y^{\prime }}^{2}-3 x y^{\frac {2}{3}} y^{\prime }+9 y^{\frac {5}{3}} = 0 \]

4069

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

4070

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

4071

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

4072

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

4073

\[ {}2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right ) = 0 \]

4074

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

4075

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

4076

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

4077

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

4078

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

4079

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

4080

\[ {}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \]

4081

\[ {}9 {y^{\prime }}^{2}+3 y^{4} y^{\prime } x +y^{5} = 0 \]

4082

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

4083

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

4084

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

4085

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

4086

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

4087

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

4088

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

4089

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

4090

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

4091

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

4092

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

4093

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

4094

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

4095

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

4096

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

4097

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

4098

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

4099

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

4100

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

4101

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

4102

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

4103

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

4104

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

4105

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

4106

\[ {}x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0 \]

4107

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

4108

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

4109

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

4110

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

4111

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

4112

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

4113

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

4114

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

4115

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

4116

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

4117

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

4118

\[ {}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \]