ODE
\[ y'(x)=x \csc (x)-y(x) \cot (x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.164195 (sec), leaf count = 19
\[\left \{\left \{y(x)\to \frac {1}{2} \left (x^2+2 c_1\right ) \csc (x)\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 16
\[\left [y \left (x \right ) = \frac {\frac {x^{2}}{2}+\textit {\_C1}}{\sin \left (x \right )}\right ]\] Mathematica raw input
DSolve[y'[x] == x*Csc[x] - Cot[x]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> ((x^2 + 2*C[1])*Csc[x])/2}}
Maple raw input
dsolve(diff(y(x),x) = x*csc(x)-y(x)*cot(x), y(x))
Maple raw output
[y(x) = (1/2*x^2+_C1)/sin(x)]