5.20.32 Problems 3101 to 3200

Table 5.969: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

16966

\[ {}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y = 0 \]

16967

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

16968

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

16969

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

16970

\[ {}y^{\left (5\right )} = 0 \]

16971

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

16972

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

16973

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

16974

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

16975

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

16976

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

16977

\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \]

16978

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \]

16979

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x} \]

16980

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

16981

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

16982

\[ {}y^{\prime \prime }+25 y = \cos \left (5 x \right ) \]

16983

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

16984

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

16985

\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

16986

\[ {}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \]

16987

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right ) \]

16988

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

16989

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

16990

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

16991

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1 \]

16992

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

16993

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

16994

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

16995

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

16996

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

16997

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

16998

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

16999

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

17000

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

17001

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

17002

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

17003

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

17004

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

17005

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

17006

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

17007

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right ) \]

17008

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \]

17009

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x} \]

17010

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

17011

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

17012

\[ {}y^{\prime \prime }+9 y = 9 \]

17013

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

17014

\[ {}5 y^{\prime \prime \prime }-7 y^{\prime \prime } = 3 \]

17015

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

17016

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

17017

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

17018

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

17019

\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \]

17020

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

17021

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x} \]

17022

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x} \]

17023

\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \]

17024

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

17025

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x} \]

17026

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

17027

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

17028

\[ {}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

17029

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

17030

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

17031

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

17032

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

17033

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

17034

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

17035

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

17036

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

17037

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

17038

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

17039

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

17040

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

17041

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

17042

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

17043

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

17044

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

17045

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

17046

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

17047

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

17048

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

17049

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \]

17050

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

17051

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

17052

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

17053

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

17054

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

17055

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

17056

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

17057

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

17058

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

17059

\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \]

17060

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

17061

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x} \]

17062

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \]

17063

\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \]

17064

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

17065

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