Internal problem ID [5748]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 The Unit Step and Impulse Functions. Page
303
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-t^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-y(t)=t^2,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-t}+{\mathrm e}^{t}-t^{2}-2 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[{y''[t]-y[t]==t^2,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t^2+2 \cosh (t)-2 \\ \end{align*}