ODE No. 175

\[ a x^3+\left (x^2-1\right ) x y'(x)-\left (2 x^2-1\right ) y(x)=0 \]

✓ Mathematica : cpu = 0.0249135 (sec), leaf count = 24

DSolve[a*x^3 - (-1 + 2*x^2)*y[x] + x*(-1 + x^2)*Derivative[1][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to a x+c_1 \sqrt {1-x^2} x\right \}\right \}\]

✓ Maple : cpu = 0.02 (sec), leaf count = 20

dsolve(x*(x^2-1)*diff(y(x),x)-(2*x^2-1)*y(x)+a*x^3 = 0,y(x))

\[y \left (x \right ) = x \left (\sqrt {x -1}\, \sqrt {1+x}\, c_{1} +a \right )\]