Internal problem ID [4933]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {81}{10}}, y^{\prime }\relax (0) = {\frac {39}{10}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=0,y(0) = 81/10, D(y)(0) = 39/10],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (81-123 t \right ) {\mathrm e}^{2 t}}{10} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 19
DSolve[{y''[t]-4*y'[t]+4*y[t]==0,{y[0]==81/10,y'[0]==39/10}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {3}{10} e^{2 t} (41 t-27) \\ \end{align*}