Internal problem ID [10857]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-\sin \left (3 x \right ) \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)=sin(3*x)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )-\frac {\sin \left (2 x \right )}{6}-\frac {\sin \left (4 x \right )}{30} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 30
DSolve[y''[x]+y[x]==Sin[3*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (x)-\frac {1}{15} \sin (x) (6 \cos (x)+\cos (3 x)-15 c_2) \\ \end{align*}