Internal problem ID [4110]
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 21.16, 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 }+4 y-x \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+4*y(x)=x*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\frac {x \sin \left (2 x \right )}{16}-\frac {\cos \left (2 x \right ) x^{2}}{8} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 38
DSolve[y''[x]+4*y[x]==x*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{64} \left (\left (-8 x^2+1+64 c_1\right ) \cos (2 x)+4 (x+16 c_2) \sin (2 x)\right ) \\ \end{align*}