4.3.45 Problems 4401 to 4500

Table 4.373: Second order ode

#

ODE

Mathematica

Maple

Sympy

13950

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

13951

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

13952

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

13953

\[ {} 4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]

13954

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

13955

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

13956

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]

13957

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

13958

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

13960

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

13961

\[ {} y^{\prime \prime }-20 y^{\prime }+51 y = 0 \]

13962

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

13963

\[ {} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \]

13964

\[ {} 2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

13965

\[ {} 4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]

13966

\[ {} y^{\prime \prime }+6 y^{\prime }+34 y = 0 \]

13974

\[ {} y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \]

13975

\[ {} 4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \]

13976

\[ {} 4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \]

13977

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

13978

\[ {} y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \]

13979

\[ {} 2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \]

13980

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

13981

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

13983

\[ {} y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \]

13984

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

13985

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

13987

\[ {} 3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \]

13990

\[ {} y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]

13991

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

13992

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

13993

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \]

13994

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \]

13995

\[ {} y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (-4+t \right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (-4+t \right ) \]

13996

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

13997

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

13998

\[ {} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]

13999

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \]

14000

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \]

14001

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \]

14002

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \]

14003

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

14004

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

14005

\[ {} y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \]

14006

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

14007

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right ) \]

14008

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right ) \]

14016

\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

14017

\[ {} t^{2} y^{\prime \prime }-6 t y^{\prime }+y \sin \left (2 t \right ) = \ln \left (t \right ) \]

14018

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

14019

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

14020

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

14021

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

14022

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t} \]

14023

\[ {} y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

14025

\[ {} 3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2} \]

14059

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

14060

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

14061

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

14062

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

14063

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

14064

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

14065

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

14066

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

14075

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

14076

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

14077

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

14078

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

14079

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

14080

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

14081

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

14082

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

14088

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

14089

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

14090

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

14155

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

14157

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

14158

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

14159

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

14160

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

14161

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

14162

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

14163

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

14166

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

14167

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

14168

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

14169

\[ {} y^{\prime \prime }+12 y = 7 y^{\prime } \]

14170

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

14171

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

14172

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

14173

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

14174

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

14183

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = x \]

14184

\[ {} s^{\prime \prime }-a^{2} s = t +1 \]

14185

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

14186

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

14187

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

14188

\[ {} y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

14189

\[ {} y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

14190

\[ {} y^{\prime \prime }-3 y^{\prime } = 2-6 x \]