Internal problem ID [11012]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 2(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 y^{\prime \prime }+5 y^{\prime }-2 y-3 t^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(3*diff(y(t),t$2)+5*diff(y(t),t)-2*y(t)=3*t^2,y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-2 t}+{\mathrm e}^{\frac {t}{3}} c_{1} -\frac {3 t^{2}}{2}-\frac {15 t}{2}-\frac {93}{4} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 36
DSolve[3*y''[t]+5*y'[t]-2*y[t]==3*t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {3}{4} (2 t (t+5)+31)+c_1 e^{t/3}+c_2 e^{-2 t} \\ \end{align*}