4.1.19 \(y'(x)=y(x) \cot (x)+e^x \sin (x)\)

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

\[ \left \{ y \relax (x ) =\sin \relax (x ) \left ({{\rm e}^{x}}+{\it \_C1} \right ) \right \} \] 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)