4.51 Problems 5001 to 5100

Table 4.101: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

5001

\[ {}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]

5002

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

5003

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

5004

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

5005

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

5006

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

5007

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

5008

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

5009

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

5010

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

5011

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

5012

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

5013

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

5014

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

5015

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

5016

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

5017

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

5018

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

5019

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

5020

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

5021

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

5022

\[ {}\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \]

5023

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

5024

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

5025

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

5026

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

5027

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

5028

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

5029

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

5030

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

5031

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

5032

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

5033

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

5034

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

5035

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

5036

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

5037

\[ {}w^{\prime }+w x = {\mathrm e}^{x} \]

5038

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

5039

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

5040

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

5041

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

5042

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

5043

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

5044

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

5045

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

5046

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

5047

\[ {}x^{\prime \prime }+42 x^{\prime }+x = 0 \]

5048

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

5049

\[ {}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \]

5050

\[ {}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

5051

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

5052

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

5053

\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]

5054

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

5055

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

5056

\[ {}x^{2} y^{\prime }+2 x y-x +1 = 0 \]

5057

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

5058

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

5059

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

5060

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

5061

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

5062

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

5063

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

5064

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

5065

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

5066

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

5067

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

5068

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

5069

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

5070

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

5071

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

5072

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

5073

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

5074

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

5075

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

5076

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

5077

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

5078

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

5079

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

5080

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

5081

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

5082

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

5083

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

5084

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

5085

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

5086

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

5087

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

5088

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

5089

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

5090

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

5091

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

5092

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

5093

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

5094

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

5095

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

5096

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

5097

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

5098

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

5099

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

5100

\[ {}\left (x^{2}+1\right ) y^{\prime }+3 x y = 5 x \]