Internal problem ID [7671]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y^{\prime }+y-x \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x) + y(x) - x*sin(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-x \cos \relax (x )+\sin \relax (x )+c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 19
DSolve[x*y'[x]+ y[x] - x*Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sin (x)-x \cos (x)+c_1}{x} \\ \end{align*}