6.131 Problems 13001 to 13100

Table 6.261: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

13001

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

13002

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

13003

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

13004

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

13005

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

13006

\[ {} \theta ^{\prime } = -a \theta +{\mathrm e}^{b t} \]

13007

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

13008

\[ {} x^{\prime }+\frac {5 x}{t} = t +1 \]

13009

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

13010

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

13011

\[ {} N^{\prime } = N-9 \,{\mathrm e}^{-t} \]

13012

\[ {} \cos \left (\theta \right ) v^{\prime }+v = 3 \]

13013

\[ {} R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \]

13014

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

13015

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

13016

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

13017

\[ {} x^{\prime \prime }+x^{\prime } = 3 t \]

13018

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

13019

\[ {} x^{\prime } = a x+b \]

13020

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

13021

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

13022

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

13023

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

13024

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

13025

\[ {} x^{\prime } = a x+b x^{3} \]

13026

\[ {} w^{\prime } = t w+t^{3} w^{3} \]

13027

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

13028

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

13029

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

13030

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

13031

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

13032

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

13033

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

13034

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

13035

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

13036

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

13037

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

13038

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

13039

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

13040

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

13041

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

13042

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

13043

\[ {} x^{\prime \prime }+9 x = 0 \]

13044

\[ {} x^{\prime \prime }-12 x = 0 \]

13045

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

13046

\[ {} \frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0 \]

13047

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

13048

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0 \]

13049

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

13050

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

13051

\[ {} x^{\prime \prime }+x^{\prime }+x = 12 \]

13052

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

13053

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \]

13054

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

13055

\[ {} x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \]

13056

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

13057

\[ {} x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t} \]

13058

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t} \]

13059

\[ {} x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right ) \]

13060

\[ {} x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \]

13061

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

13062

\[ {} x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \]

13063

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

13064

\[ {} x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2} \]

13065

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

13066

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

13067

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

13068

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

13069

\[ {} x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \]

13070

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

13071

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

13072

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \]

13073

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

13074

\[ {} x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \]

13075

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

13076

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

13077

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

13078

\[ {} t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \]

13079

\[ {} t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \]

13080

\[ {} t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0 \]

13081

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

13082

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

13083

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

13084

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

13085

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

13086

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

13087

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

13088

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

13089

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

13090

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

13091

\[ {} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

13092

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

13093

\[ {} x^{\prime \prime }+t x^{\prime }+x = 0 \]

13094

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

13095

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

13096

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

13097

\[ {} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0 \]

13098

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

13099

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

13100

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