14.11.15 problem 15

Internal problem ID [2608]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
Problem number : 15
Date solved : Monday, January 27, 2025 at 06:04:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

\[ y = -\frac {\cos \left (t \right )^{3}}{4}+\frac {\left (8 c_1 +3\right ) \cos \left (t \right )}{8}+\frac {\sin \left (t \right ) \left (t +4 c_2 \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 35

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

\[ y(t)\to -\frac {1}{16} \cos (3 t)+\left (\frac {1}{8}+c_1\right ) \cos (t)+\frac {1}{4} (t+4 c_2) \sin (t) \]