66.2.42 problem Problem 57

Internal problem ID [13941]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 57
Date solved : Tuesday, January 28, 2025 at 06:09:14 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -\frac {\sin \left (2 x \right )}{6}-\frac {\sin \left (4 x \right )}{30} \]

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 30

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

\[ y(x)\to c_1 \cos (x)-\frac {1}{15} \sin (x) (6 \cos (x)+\cos (3 x)-15 c_2) \]