6.151 Problems 15001 to 15100

Table 6.301: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

15001

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

15002

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

15003

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

15004

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

15005

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

15006

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

15007

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

15008

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

15009

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

15010

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

15011

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

15012

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

15013

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

15014

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

15015

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

15016

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

15017

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

15018

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

15019

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

15020

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

15021

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

15022

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

15023

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

15024

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

15025

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

15026

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

15027

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

15028

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

15029

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

15030

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

15031

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

15032

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

15033

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

15034

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

15035

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

15036

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

15037

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

15038

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

15039

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

15040

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

15041

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

15042

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

15043

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

15044

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

15045

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

15046

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

15047

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

15048

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

15049

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

15050

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

15051

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

15052

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

15053

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

15054

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

15055

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

15056

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

15057

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

15058

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

15059

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

15060

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

15061

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

15062

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

15063

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

15064

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

15065

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

15066

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

15067

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

15068

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

15069

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

15070

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

15071

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

15072

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

15073

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

15074

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

15075

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

15076

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

15077

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

15078

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

15079

\[ {} 6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0 \]

15080

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

15081

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

15082

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

15083

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

15084

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

15085

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

15086

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

15087

\[ {} 4 x y-6+x^{2} y^{\prime } = 0 \]

15088

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

15089

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

15090

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

15091

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

15092

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

15093

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

15094

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

15095

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

15096

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

15097

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

15098

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

15099

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

15100

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