Internal problem ID [835]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+2*y(t)=0,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \sin \relax (t ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 11
DSolve[{y''[t]-2*y'[t]+2*y[t]==0,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t \sin (t) \\ \end{align*}