6.161 Problems 16001 to 16100

Table 6.321: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

16001

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

16002

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

16003

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

16004

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

16005

\[ {} y^{\prime } = y \cos \left (\frac {\pi y}{2}\right ) \]

16006

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

16007

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

16008

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

16009

\[ {} y^{\prime } = \cos \left (\frac {\pi y}{2}\right ) \]

16010

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

16011

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

16012

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

16013

\[ {} y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \]

16014

\[ {} y^{\prime } = -4 y+3 \,{\mathrm e}^{-t} \]

16015

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

16016

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

16017

\[ {} y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t} \]

16018

\[ {} y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \]

16019

\[ {} y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}} \]

16020

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

16021

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

16022

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

16023

\[ {} -2 y+y^{\prime } = 7 \,{\mathrm e}^{2 t} \]

16024

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

16025

\[ {} y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t} \]

16026

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

16027

\[ {} y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t} \]

16028

\[ {} y+y^{\prime } = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \]

16029

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

16030

\[ {} y^{\prime } = \frac {3 y}{t}+t^{5} \]

16031

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

16032

\[ {} y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \]

16033

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

16034

\[ {} y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t} \]

16035

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

16036

\[ {} y^{\prime } = \frac {y}{t +1}+4 t^{2}+4 t \]

16037

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

16038

\[ {} y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \]

16039

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

16040

\[ {} y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t} \]

16041

\[ {} y^{\prime } = \sin \left (t \right ) y+4 \]

16042

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

16043

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

16044

\[ {} y^{\prime } = y+4 \cos \left (t^{2}\right ) \]

16045

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

16046

\[ {} y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t \]

16047

\[ {} y^{\prime } = a t y+4 \,{\mathrm e}^{-t^{2}} \]

16048

\[ {} y^{\prime } = t^{r} y+4 \]

16049

\[ {} v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right ) \]

16050

\[ {} y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \]

16051

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

16052

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

16053

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

16054

\[ {} y^{\prime } = -\sin \left (y\right )^{5} \]

16055

\[ {} y^{\prime } = \frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \]

16056

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

16057

\[ {} y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \]

16058

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

16059

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

16060

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

16061

\[ {} y^{\prime } = 3 y+{\mathrm e}^{7 t} \]

16062

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

16063

\[ {} y^{\prime } = -5 y+\sin \left (3 t \right ) \]

16064

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

16065

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

16066

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

16067

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

16068

\[ {} x^{\prime } = -t x \]

16069

\[ {} y^{\prime } = 2 y+\cos \left (4 t \right ) \]

16070

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

16071

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

16072

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

16073

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

16074

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

16075

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

16076

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

16077

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

16078

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

16079

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

16080

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

16081

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

16082

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

16083

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

16084

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

16085

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

16086

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

16087

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

16088

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

16089

\[ {} \left [x^{\prime }\left (t \right ) = 3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 \pi y \left (t \right )-\frac {x \left (t \right )}{3}\right ] \]

16090

\[ {} \left [p^{\prime }\left (t \right ) = 3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right ), q^{\prime }\left (t \right ) = -2 p \left (t \right )+6 r \left (t \right ), r^{\prime }\left (t \right ) = \frac {73 q \left (t \right )}{100}+2 r \left (t \right )\right ] \]

16091

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

16092

\[ {} [x^{\prime }\left (t \right ) = \beta y \left (t \right ), y^{\prime }\left (t \right ) = \gamma x \left (t \right )-y \left (t \right )] \]

16093

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

16094

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

16095

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )] \]

16096

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

16097

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

16098

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

16099

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

16100

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