ODE
\[ x \left (1-x^2\right ) y''(x)-y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.015015 (sec), leaf count = 23
\[\left \{\left \{y(x)\to c_2-c_1 \sqrt {1-x^2}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\it \_C1}+\sqrt {{x}^{2}-1}{\it \_C2} \right \} \] Mathematica raw input
DSolve[-y'[x] + x*(1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[1 - x^2]*C[1]) + C[2]}}
Maple raw input
dsolve(x*(-x^2+1)*diff(diff(y(x),x),x)-diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+(x^2-1)^(1/2)*_C2