Internal problem ID [4935]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y}{25}-\frac {t^{2}}{50}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -25, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 11
dsolve([diff(y(t),t$2)+4/100*y(t)=2/100*t^2,y(0) = -25, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {t^{2}}{2}-25 \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 14
DSolve[{y''[t]+4/100*y[t]==2/100*t^2,{y[0]==-25,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (t^2-50\right ) \\ \end{align*}