Internal problem ID [14537]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {8 y^{\prime \prime }+6 y^{\prime }+y=5 t^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(8*diff(y(t),t$2)+6*diff(y(t),t)+y(t)=5*t^2,y(t), singsol=all)
\[ y \left (t \right ) = -4 \,{\mathrm e}^{-\frac {t}{2}} c_{1} +{\mathrm e}^{-\frac {t}{4}} c_{2} +5 t^{2}-60 t +280 \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 35
DSolve[8*y''[t]+6*y'[t]+y[t]==5*t^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 5 t^2-60 t+c_1 e^{-t/4}+c_2 e^{-t/2}+280 \]