11.3.8 problem 15

Internal problem ID [1490]
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
Date solved : Monday, January 27, 2025 at 04:57:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+\omega ^{2} y&=\cos \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.283 (sec). Leaf size: 27

dsolve([diff(y(t),t$2)+omega^2*y(t)=cos(2*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {\cos \left (2 t \right )+\cos \left (\omega t \right ) \left (\omega ^{2}-5\right )}{\omega ^{2}-4} \]

✓ Solution by Mathematica

Time used: 0.190 (sec). Leaf size: 28

DSolve[{D[y[t],{t,2}]+w^2*y[t]==Cos[2*t],{y[0]==1,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\left (w^2-5\right ) \cos (t w)+\cos (2 t)}{w^2-4} \]