26.5.6 problem 8

Internal problem ID [4280]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 8
Date solved : Monday, January 27, 2025 at 08:47:42 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 18

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

\[ y(x)\to \frac {x \sin (x)+\cos (x)+c_1}{x} \]