64.11.21 problem 21

Internal problem ID [13471]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 05:44:41 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

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

\[ y = \frac {\left (-x^{2}+4 c_{1} \right ) \cos \left (x \right )}{4}+\frac {\sin \left (x \right ) \left (4 c_{2} +x \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 54

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

\[ y(x)\to \cos (x) \int _1^x-K[1] \sin ^2(K[1])dK[1]+\sin (x) \int _1^x\cos (K[2]) K[2] \sin (K[2])dK[2]+c_1 \cos (x)+c_2 \sin (x) \]