Internal problem ID [4617]
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 21.15, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=4 \sin \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+y(x)=4*x*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-x^{2}+c_{1} \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_{2} +x \right ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 27
DSolve[y''[x]+y[x]==4*x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-x^2+\frac {1}{2}+c_1\right ) \cos (x)+(x+c_2) \sin (x) \]