14.11.16 problem 16

Internal problem ID [2609]
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 : 16
Date solved : Monday, January 27, 2025 at 06:04:29 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(diff(y(t),t$2)+y(t)=cos(t)*cos(2*t)*cos(3*t),y(t), singsol=all)
 

\[ y = -\frac {8 \cos \left (t \right )^{6}}{35}+\frac {22 \cos \left (t \right )^{4}}{105}+\cos \left (t \right ) c_1 +\sin \left (t \right ) c_2 -\frac {17 \cos \left (t \right )^{2}}{105}+\frac {34}{105} \]

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 43

DSolve[D[y[t],{t,2}]+y[t]==Cos[t]*Cos[2*t]*Cos[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {1}{12} \cos (2 t)-\frac {1}{60} \cos (4 t)-\frac {1}{140} \cos (6 t)+c_1 \cos (t)+c_2 \sin (t)+\frac {1}{4} \]