Internal problem ID [15326]
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 15.3 Nonhomogeneous linear equations with
constant coefficients. Superposition principle. Exercises page 137
Problem number: 557.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sin \left (x \right ) \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+4*y(x)=sin(x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} -\frac {2 \cos \left (x \right )}{15}+\frac {2 \cos \left (x \right )^{3}}{5} \]
✓ Solution by Mathematica
Time used: 0.178 (sec). Leaf size: 34
DSolve[y''[x]+4*y[x]==Sin[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cos (x)}{6}+\frac {1}{10} \cos (3 x)+c_1 \cos (2 x)+c_2 \sin (2 x) \]