Internal problem ID [5687]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=6 t -8} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.672 (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)
\[ y \left (t \right ) = 2 t -2 \,{\mathrm e}^{2 t} \sinh \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.013 (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]
\[ y(t)\to 2 t+e^t-e^{3 t} \]