Internal problem ID [836]
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: 11.
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 }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+4*y(t)=0,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {2 \,{\mathrm e}^{t} \left (\sqrt {3}\, \sin \left (\sqrt {3}\, t \right )-3 \cos \left (\sqrt {3}\, t \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 37
DSolve[{y''[t]-2*y'[t]+4*y[t]==0,{y[0]==2,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {2}{3} e^t \left (\sqrt {3} \sin \left (\sqrt {3} t\right )-3 \cos \left (\sqrt {3} t\right )\right ) \\ \end{align*}