Internal problem ID [4942]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+8 y-{\mathrm e}^{-3 t}+{\mathrm e}^{-5 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: 0.016 (sec). Leaf size: 27
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=exp(-3*t)-exp(-5*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\left ({\mathrm e}^{-3 t}-3 \,{\mathrm e}^{-2 t}+3 \,{\mathrm e}^{-t}-1\right ) {\mathrm e}^{-2 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 21
DSolve[{y''[t]+6*y'[t]+8*y[t]==Exp[-3*t]-Exp[-5*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-5 t} \left (e^t-1\right )^3 \\ \end{align*}