15.15.1 problem 1

Internal problem ID [3205]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:25:58 AM
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: 0.004 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 33

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

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