75.25.5 problem 761

Internal problem ID [17228]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 18.3. Finding periodic solutions of linear differential equations. Exercises page 187
Problem number : 761
Date solved : Tuesday, January 28, 2025 at 09:58:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)+9*y(x)=sin(x)^3,y(x), singsol=all)
 

\[ y = \frac {\left (x +24 c_{1} \right ) \cos \left (3 x \right )}{24}+\frac {\left (144 c_{2} -1\right ) \sin \left (3 x \right )}{144}+\frac {3 \sin \left (x \right )}{32} \]

✓ Solution by Mathematica

Time used: 0.475 (sec). Leaf size: 76

DSolve[D[y[x],{x,2}]+9*y[x]==Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (3 x) \int _1^x-\frac {1}{3} (2 \cos (2 K[1])+1) \sin ^4(K[1])dK[1]+\sin (3 x) \int _1^x\frac {1}{3} \cos (3 K[2]) \sin ^3(K[2])dK[2]+c_1 \cos (3 x)+c_2 \sin (3 x) \]