32.8.13 problem Exercise 21.16, page 231

Internal problem ID [5962]
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
Date solved : Monday, January 27, 2025 at 01:29:06 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=x \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)+4*y(x)=x*sin(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (-x^{2}+8 c_{1} \right ) \cos \left (2 x \right )}{8}+\frac {\sin \left (2 x \right ) \left (16 c_{2} +x \right )}{16} \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{64} \left (\left (-8 x^2+1+64 c_1\right ) \cos (2 x)+4 (x+16 c_2) \sin (2 x)\right ) \]