Internal problem ID [14858]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 37.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y=t^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 40
dsolve(diff(y(t),t$4)+4*diff(y(t),t$3)+14*diff(y(t),t$2)+20*diff(y(t),t)+25*y(t)=t^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {4}{625}+\left (\left (c_{3} t +c_{1} \right ) \cos \left (2 t \right )+\sin \left (2 t \right ) \left (t c_{4} +c_{2} \right )\right ) {\mathrm e}^{-t}+\frac {t^{2}}{25}-\frac {8 t}{125} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 54
DSolve[y''''[t]+4*y'''[t]+14*y''[t]+20*y'[t]+25*y[t]==t^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{625} \left (25 t^2-40 t+4\right )+e^{-t} (c_4 t+c_3) \cos (2 t)+e^{-t} (c_2 t+c_1) \sin (2 t) \]