78.8.13 problem 13

Internal problem ID [18211]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 11:39:05 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 25

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

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