Internal problem ID [4117]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.27, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\sin \left (2 x \right ) \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)=sin(2*x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}+\frac {\sin \relax (x ) \left (-\sin \relax (x ) \cos \relax (x )+x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 33
DSolve[y''[x]+y[x]==Sin[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} (\cos (3 x)+(-1+16 c_1) \cos (x)+4 (x+4 c_2) \sin (x)) \\ \end{align*}