6.161 Problems 16001 to 16100

Table 6.321: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

16001

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

16002

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

16003

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

16004

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

16005

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

16006

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

16007

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

16008

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

16009

\[ {} \cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \]

16010

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

16011

\[ {} 2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0 \]

16012

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

16013

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

16014

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

16015

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

16016

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

16017

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

16018

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

16019

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

16020

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

16021

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

16022

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

16023

\[ {} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0 \]

16024

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

16025

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

16026

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

16027

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

16028

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

16029

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

16030

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

16031

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

16032

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

16033

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

16034

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

16035

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

16036

\[ {} t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0 \]

16037

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

16038

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

16039

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

16040

\[ {} t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

16041

\[ {} 5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \]

16042

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

16043

\[ {} 2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0 \]

16044

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

16045

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

16046

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

16047

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

16048

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

16049

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

16050

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

16051

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

16052

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

16053

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

16054

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

16055

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

16056

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

16057

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

16058

\[ {} y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \]

16059

\[ {} \cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0 \]

16060

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

16061

\[ {} y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \]

16062

\[ {} y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \]

16063

\[ {} -\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime } \]

16064

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

16065

\[ {} y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \]

16066

\[ {} y^{\prime }+3 y = -10 \sin \left (t \right ) \]

16067

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

16068

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

16069

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

16070

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

16071

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

16072

\[ {} x^{\prime } = \frac {5 t x}{x^{2}+t^{2}} \]

16073

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

16074

\[ {} t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0 \]

16075

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

16076

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

16077

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

16078

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

16079

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

16080

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

16081

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

16082

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

16083

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

16084

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

16085

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

16086

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

16087

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

16088

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

16089

\[ {} {\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0 \]

16090

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

16091

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

16092

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

16093

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

16094

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

16095

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

16096

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

16097

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

16098

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

16099

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

16100

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