Internal problem ID [4130]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.8, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-4 x \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)=4*x*sin(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}-x \left (x \cos \relax (x )-\sin \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 27
DSolve[y''[x]+y[x]==4*x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-x^2+\frac {1}{2}+c_1\right ) \cos (x)+(x+c_2) \sin (x) \\ \end{align*}