Internal problem ID [4929]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-10 \,{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+9*y(t)=10*exp(-t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\sin \left (3 t \right )}{3}-\cos \left (3 t \right )+{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 25
DSolve[{y''[t]+9*y[t]==10*Exp[-t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t}+\frac {1}{3} \sin (3 t)-\cos (3 t) \\ \end{align*}