ODE
\[ y'(x)=y(x) \cot (x)+e^x \sin (x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0263516 (sec), leaf count = 14
\[\left \{\left \{y(x)\to \left (c_1+e^x\right ) \sin (x)\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 11
\[ \left \{ y \left ( x \right ) =\sin \left ( x \right ) \left ( {{\rm e}^{x}}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[y'[x] == E^x*Sin[x] + Cot[x]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (E^x + C[1])*Sin[x]}}
Maple raw input
dsolve(diff(y(x),x) = exp(x)*sin(x)+y(x)*cot(x), y(x),'implicit')
Maple raw output
y(x) = sin(x)*(exp(x)+_C1)