2.131 Problems 13001 to 13100

Table 2.261: Main lookup table

#

ODE

Mathematica result

Maple result

13001

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

13002

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

13003

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

13004

\[ {}y^{\prime } = 200 y-2 y^{2} \]

13005

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

13006

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

13007

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

13008

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

13009

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

13010

\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \]

13011

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

13012

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

13013

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

13014

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

13015

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

13016

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

13017

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

13018

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

13019

\[ {}y^{\prime } = 200 y-2 y^{2} \]

13020

\[ {}y^{\prime }-2 y = -10 \]

13021

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

13022

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

13023

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

13024

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

13025

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

13026

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

13027

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

13028

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

13029

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

13030

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

13031

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

13032

\[ {}y^{\prime } = 4 y+8 \]

13033

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

13034

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

13035

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

13036

\[ {}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y \]

13037

\[ {}y^{\prime }+2 y = 6 \]

13038

\[ {}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x} \]

13039

\[ {}y^{\prime } = 4 y+16 x \]

13040

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

13041

\[ {}x y^{\prime }+3 y-10 x^{2} = 0 \]

13042

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

13043

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

13044

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

13045

\[ {}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x} \]

13046

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

13047

\[ {}y^{\prime }-3 y = 6 \]

13048

\[ {}y^{\prime }-3 y = 6 \]

13049

\[ {}y^{\prime }+5 y = {\mathrm e}^{-3 x} \]

13050

\[ {}x y^{\prime }+3 y = 20 x^{2} \]

13051

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

13052

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

13053

\[ {}y^{\prime }+6 x y = \sin \left (x \right ) \]

13054

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

13055

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

13056

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

13057

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

13058

\[ {}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \]

13059

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

13060

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

13061

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

13062

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

13063

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

13064

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

13065

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

13066

\[ {}y^{\prime }+3 \cot \left (x \right ) y = 6 \cos \left (x \right ) y^{\frac {2}{3}} \]

13067

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

13068

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

13069

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

13070

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

13071

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

13072

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

13073

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

13074

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

13075

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

13076

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

13077

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

13078

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

13079

\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \]

13080

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

13081

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

13082

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

13083

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

13084

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

13085

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

13086

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

13087

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

13088

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

13089

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

13090

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

13091

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

13092

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

13093

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

13094

\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \]

13095

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

13096

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

13097

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

13098

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

13099

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

13100

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