ODE
\[ x y'(x)=x^2 \sin (x)+y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0101323 (sec), leaf count = 14
\[\left \{\left \{y(x)\to x \left (c_1-\cos (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 12
\[ \left \{ y \left ( x \right ) =x \left ( -\cos \left ( x \right ) +{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[x*y'[x] == x^2*Sin[x] + y[x],y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] - Cos[x])}}
Maple raw input
dsolve(x*diff(y(x),x) = x^2*sin(x)+y(x), y(x),'implicit')
Maple raw output
y(x) = x*(-cos(x)+_C1)