3.9.28 Problems 2701 to 2800

Table 3.561: First order ode linear in derivative

#

ODE

Mathematica

Maple

5887

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

5888

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

5892

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

5893

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

5894

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

5895

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

5896

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

5912

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

5915

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

5916

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

5920

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

5922

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

5923

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

5924

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

5925

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

5926

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

5927

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

5928

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

5929

\[ {}L y^{\prime }+R y = E \]

5930

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

5931

\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]

5932

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

5933

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

5934

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

5935

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

5936

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

5937

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

5938

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

5939

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

5940

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

5941

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

5942

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

5943

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

6063

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

6064

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

6065

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

6066

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

6067

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

6068

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

6069

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

6070

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

6071

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

6072

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

6073

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

6074

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

6075

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

6076

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

6077

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

6078

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

6079

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

6080

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

6081

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

6082

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

6083

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

6084

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

6085

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

6086

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

6087

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

6088

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

6089

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

6090

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

6105

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

6106

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

6107

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

6108

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

6111

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

6112

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

6113

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

6114

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

6116

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

6117

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

6118

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

6119

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

6120

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

6121

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

6122

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

6123

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

6124

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

6125

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

6126

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

6127

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

6128

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

6129

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

6130

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

6131

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

6132

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

6133

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

6134

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

6135

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

6137

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

6139

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

6140

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

6141

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

6142

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

6143

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

6144

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

6145

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

6146

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

6147

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

6148

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