ODE
\[ (1-x \cot (x)) y''(x)-x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.27977 (sec), leaf count = 15
\[\{\{y(x)\to c_1 x+c_2 \sin (x)\}\}\]
Maple ✓
cpu = 3.037 (sec), leaf count = 81
\[\left [y \left (x \right ) = x \textit {\_C2} +\textit {\_C1} x \left (-\frac {i {\mathrm e}^{2 i x}}{2 \sqrt {\frac {{\mathrm e}^{2 i x}}{\left ({\mathrm e}^{2 i x}+1\right )^{2}}}\, \left ({\mathrm e}^{2 i x}+1\right ) x}+\frac {i}{2 \sqrt {\frac {{\mathrm e}^{2 i x}}{\left ({\mathrm e}^{2 i x}+1\right )^{2}}}\, \left ({\mathrm e}^{2 i x}+1\right ) x}\right )\right ]\] Mathematica raw input
DSolve[y[x] - x*y'[x] + (1 - x*Cot[x])*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + C[2]*Sin[x]}}
Maple raw input
dsolve((1-x*cot(x))*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = x*_C2+_C1*x*(-1/2*I/(exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)/(exp(2*I*x)+1)*exp(2*I*x)/x+1/2*I/(exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)/(exp(2*I*x)+1)/x)]