Internal problem ID [12904]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 6. Laplace transform. Section 6.3 page 600
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y={\mathrm e}^{2 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 22
dsolve([diff(y(t),t$2)-4*y(t)=exp(2*t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y = \frac {13 \,{\mathrm e}^{-2 t}}{16}+\frac {{\mathrm e}^{2 t} \left (3+4 t \right )}{16} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 27
DSolve[{y''[t]-4*y[t]==Exp[2*t],{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{16} e^{-2 t} \left (e^{4 t} (4 t+3)+13\right ) \]