4.7.31 \(2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0\)

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 = 0.0381775 (sec), leaf count = 18

\[\left \{\left \{y(x)\to c_1 \csc (x)-\frac {1}{2 x}\right \}\right \}\]

Maple
cpu = 0.057 (sec), leaf count = 16

\[ \left \{ y \relax (x ) =-{\frac {1}{2\,x}}+{\frac {{\it \_C1}}{\sin \relax (x ) }} \right \} \] 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*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),'implicit')

Maple raw output

y(x) = -1/2/x+1/sin(x)*_C1