Internal problem ID [4940]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }-4 y-6 \,{\mathrm e}^{2 t -3}=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {3}{2}\right ) = 4, y^{\prime }\left (\frac {3}{2}\right ) = 5\right ] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+3*diff(y(t),t)-4*y(t)=6*exp(2*t-3),y(3/2) = 4, D(y)(3/2) = 5],y(t), singsol=all)
\[ y \relax (t ) = 3 \,{\mathrm e}^{t -\frac {3}{2}}+{\mathrm e}^{2 t -3} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 22
DSolve[{y''[t]+3*y'[t]-4*y[t]==6*Exp[2*t-3],{y[15/10]==4,y'[15/10]==5}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 3 e^{t-\frac {3}{2}}+e^{2 t-3} \\ \end{align*}