78.14.12 problem 4 (d)

Internal problem ID [18348]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 19. The Method of Variation of Parameters. Problems at page 135
Problem number : 4 (d)
Date solved : Tuesday, January 28, 2025 at 11:47:58 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 34

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

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