6.151 Problems 15001 to 15100

Table 6.301: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

15001

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

15002

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

15003

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

15004

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

15005

\[ {} x^{\prime }+p x = q \]

15006

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

15007

\[ {} i^{\prime } = p \left (t \right ) i \]

15008

\[ {} x^{\prime } = \lambda x \]

15009

\[ {} m v^{\prime } = -m g +k v^{2} \]

15010

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

15011

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

15012

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

15013

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

15014

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

15015

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

15016

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

15017

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

15018

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

15019

\[ {} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \]

15020

\[ {} T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

15021

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

15022

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

15023

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

15024

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

15025

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

15026

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

15027

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

15028

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

15029

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

15030

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

15031

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

15032

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

15033

\[ {} z^{\prime \prime }-4 z^{\prime }+13 z = 0 \]

15034

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

15035

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

15036

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

15037

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

15038

\[ {} 2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]

15039

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

15040

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]

15041

\[ {} 4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]

15042

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

15043

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

15044

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

15045

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

15046

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

15047

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

15048

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

15049

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

15050

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

15051

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

15052

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

15053

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

15054

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

15055

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

15056

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

15057

\[ {} x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

15058

\[ {} x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

15059

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

15060

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

15061

\[ {} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \]

15062

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

15063

\[ {} x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right ) \]

15064

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

15065

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

15066

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

15067

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

15068

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

15069

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

15070

\[ {} \tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0 \]

15071

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

15072

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

15073

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

15074

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

15075

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

15076

\[ {} \left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \]

15077

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

15078

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

15079

\[ {} t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \]

15080

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

15081

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

15082

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

15083

\[ {} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

15084

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

15085

\[ {} 3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]

15086

\[ {} t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]

15087

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

15088

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

15089

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

15090

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

15091

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

15092

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

15093

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

15094

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

15095

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

15096

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

15097

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

15098

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

15099

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

15100

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}] \]