82.32.1 problem Ex. 2

Internal problem ID [18892]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 80
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:33:44 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

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

\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} -\frac {2 \cos \left (x \right )}{9}+\frac {\sin \left (x \right ) x}{3} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 33

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

\[ y(x)\to \frac {1}{3} x \sin (x)+c_1 \cos (2 x)+\cos (x) \left (-\frac {2}{9}+2 c_2 \sin (x)\right ) \]