Internal problem ID [15498]
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 ODE’s). Section 18.3. Finding periodic solutions of linear
differential equations. Exercises page 187
Problem number: 761.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\sin \left (x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.205 (sec). Leaf size: 40
DSolve[y''[x]+9*y[x]==Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 \sin (x)}{32}-\frac {1}{144} \sin (3 x)+\left (\frac {x}{24}+c_1\right ) \cos (3 x)+c_2 \sin (3 x) \]