ODE
\[ 2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0 \] ODE Classification
[_linear]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.189144 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -\frac {1}{2 x}+c_1 \csc (x)\right \}\right \}\]
Maple ✓
cpu = 0.039 (sec), leaf count = 16
\[\left [y \left (x \right ) = -\frac {1}{2 x}+\frac {\textit {\_C1}}{\sin \left (x \right )}\right ]\] Mathematica raw input
DSolve[-1 + x*Cot[x] + 2*x^2*Cot[x]*y[x] + 2*x^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*1/x + C[1]*Csc[x]}}
Maple raw input
dsolve(2*x^2*diff(y(x),x)+x*cot(x)-1+2*x^2*y(x)*cot(x) = 0, y(x))
Maple raw output
[y(x) = -1/2/x+1/sin(x)*_C1]