Internal problem ID [4934]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+3 y-6 t +8=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=6*t-8,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -{\mathrm e}^{3 t}+{\mathrm e}^{t}+2 t \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 19
DSolve[{y''[t]-4*y'[t]+3*y[t]==6*t-8,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 t+e^t-e^{3 t} \\ \end{align*}