32.8.12 problem Exercise 21.15, page 231

Internal problem ID [5961]
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
Date solved : Monday, January 27, 2025 at 01:29:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=4 x \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.043 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]+y[x]==4*x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (-x^2+\frac {1}{2}+c_1\right ) \cos (x)+(x+c_2) \sin (x) \]