8.20 problem Exercise 21.27, page 231

Internal problem ID [4625]

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]]

\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right ) \sin \left (2 x \right )} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 26

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

\[ y \left (x \right ) = -\frac {\sin \left (x \right )^{2} \cos \left (x \right )}{4}+\frac {\left (4 c_{2} +x \right ) \sin \left (x \right )}{4}+\cos \left (x \right ) c_{1} \]

Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 33

DSolve[y''[x]+y[x]==Sin[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} (\cos (3 x)+(-1+16 c_1) \cos (x)+4 (x+4 c_2) \sin (x)) \]