Internal problem ID [5695]
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]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y={\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.812 (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)
\[ y \left (t \right ) = {\mathrm e}^{-4 t}-{\mathrm e}^{-3 t}-\frac {{\mathrm e}^{-5 t}}{3}+\frac {{\mathrm e}^{-2 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.113 (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]
\[ y(t)\to \frac {1}{3} e^{-5 t} \left (e^t-1\right )^3 \]