74.11.7 problem 19

Internal problem ID [16257]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 08:58:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(t),t$2)+y(t)=cos(2*t),y(t), singsol=all)
 

\[ y = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} -\frac {\cos \left (2 t \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 55

DSolve[D[y[t],{t,2}]+y[t]==Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \cos (t) \int _1^t-\cos (2 K[1]) \sin (K[1])dK[1]+\sin (t) \int _1^t\cos (K[2]) \cos (2 K[2])dK[2]+c_1 \cos (t)+c_2 \sin (t) \]