4.9.78 Problems 7701 to 7800

Table 4.993: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

21923

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

21924

\[ {} 3 x^{2}+2 x y+4 y^{2}+\left (20 x^{2}+6 x y+y^{2}\right ) y^{\prime } = 0 \]

21925

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

21926

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

21927

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

21928

\[ {} 2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime } = 0 \]

21929

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

21930

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

21931

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

21932

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

21933

\[ {} 4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime } = 0 \]

21934

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

21935

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

21936

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

21937

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

21938

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

21939

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

21940

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

21941

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

21942

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

21943

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

21944

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

21945

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

21946

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

21947

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

21948

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

21949

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

21950

\[ {} 2+3 x -5 y+7 y^{\prime } = 0 \]

21951

\[ {} 4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime } = 0 \]

21952

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

21953

\[ {} 2 x -y-1+\left (3 x +2 y-5\right ) y^{\prime } = 0 \]

21954

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

21955

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

21956

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

21957

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

21958

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

21959

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

21960

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

21961

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

21962

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

21963

\[ {} R q^{\prime }+\frac {q}{c} = E \]

21964

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

21965

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

21966

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

21967

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

21968

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

21969

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

22042

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

22043

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

22044

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

22045

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

22046

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

22081

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

22082

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

22088

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

22089

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

22090

\[ {} y^{\prime } = 5 \]

22091

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

22092

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

22093

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

22094

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

22095

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

22096

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

22097

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

22098

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

22099

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

22100

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

22101

\[ {} y^{\prime } = 2 \sqrt {{| y|}} \]

22102

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

22103

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

22104

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

22105

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

22106

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

22107

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

22108

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

22109

\[ {} y^{\prime } = 5 y \]

22110

\[ {} y^{\prime } = \frac {1+x}{1+y^{4}} \]

22111

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

22112

\[ {} x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime } = 0 \]

22113

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

22114

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

22115

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

22116

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

22117

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

22118

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

22119

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

22120

\[ {} x \,{\mathrm e}^{x}+\left (y^{5}-1\right ) y^{\prime } = 0 \]

22121

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

22122

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

22123

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

22124

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

22125

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

22126

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

22127

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

22128

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

22129

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

22130

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

22131

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

22132

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

22133

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