Internal problem ID [841]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 6.2, The Laplace Transform. Solution of Initial Value Problems. page
255
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+2 y-{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+2*y(t)=exp(-t),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (-\cos \relax (t )+7 \sin \relax (t )\right ) {\mathrm e}^{t}}{5}+\frac {{\mathrm e}^{-t}}{5} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 27
DSolve[{y''[t]-2*y'[t]+2*y[t]==Exp[-t],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{5} \left (e^{-t}-e^t (\cos (t)-7 \sin (t))\right ) \\ \end{align*}