ODE
\[ x y'(x)=x \sin (x)-y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0119053 (sec), leaf count = 19
\[\left \{\left \{y(x)\to \frac {c_1+\sin (x)-x \cos (x)}{x}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\frac {\sin \left ( x \right ) -x\cos \left ( x \right ) +{\it \_C1}}{x}} \right \} \] Mathematica raw input
DSolve[x*y'[x] == x*Sin[x] - y[x],y[x],x]
Mathematica raw output
{{y[x] -> (C[1] - x*Cos[x] + Sin[x])/x}}
Maple raw input
dsolve(x*diff(y(x),x) = x*sin(x)-y(x), y(x),'implicit')
Maple raw output
y(x) = (sin(x)-x*cos(x)+_C1)/x