Internal problem ID [5214]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 1(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-2 \sin \left (2 x \right ) \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)=2*sin(x)*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}+\frac {\sin \relax (x ) \left (-\sin \relax (x ) \cos \relax (x )+x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 33
DSolve[y''[x]+y[x]==2*Sin[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} (\cos (3 x)+(-1+8 c_1) \cos (x)+4 (x+2 c_2) \sin (x)) \\ \end{align*}