4.9.35 Problems 3401 to 3500

Table 4.907: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

8883

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

8884

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

8885

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

8886

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

8887

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

8888

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

8889

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

8890

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

8891

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

8892

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

8893

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

8894

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

8895

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

8896

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

8897

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

9017

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

9018

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

9019

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

9020

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

9021

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

9022

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

9023

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

9024

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

9025

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

9026

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

9027

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

9028

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

9029

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

9030

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

9031

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

9032

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

9033

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

9034

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

9035

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

9036

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

9037

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

9038

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

9039

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

9040

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

9041

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

9042

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

9043

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

9044

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

9059

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

9060

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

9061

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

9062

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

9065

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

9066

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

9067

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

9068

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

9070

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

9071

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

9072

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

9073

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

9074

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

9075

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

9076

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

9077

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

9078

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

9079

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

9080

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

9081

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

9082

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

9083

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

9084

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

9085

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

9086

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

9087

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

9088

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

9089

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

9091

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

9093

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

9094

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

9095

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

9096

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

9097

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

9098

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

9099

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

9100

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

9101

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

9102

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

9103

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

9104

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

9105

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

9106

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

9107

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

9108

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

9111

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

9112

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

9113

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

9114

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

9115

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

9116

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

9117

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

9118

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

9119

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

9120

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

9121

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

9122

\[ {} y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}} \]