Internal problem ID [840]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\omega ^{2} y-\cos \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 31
dsolve([diff(y(t),t$2)+omega^2*y(t)=cos(2*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\cos \left (\omega t \right ) \omega ^{2}-5 \cos \left (\omega t \right )+\cos \left (2 t \right )}{\omega ^{2}-4} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 28
DSolve[{y''[t]+w^2*y[t]==Cos[2*t],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\left (w^2-5\right ) \cos (t w)+\cos (2 t)}{w^2-4} \\ \end{align*}