\[ \left (\frac {a x}{\sqrt {b^2-x^2}}-x\right ) y'(x)^2+x y(x) y''(x)-y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.301961 (sec), leaf count = 55
DSolve[-(y[x]*Derivative[1][y][x]) + (-x + (a*x)/Sqrt[b^2 - x^2])*Derivative[1][y][x]^2 + x*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 \exp \left (\frac {\sqrt {b^2-x^2}}{a}+\frac {c_1 \log \left (a \sqrt {b^2-x^2}-c_1\right )}{a^2}\right )\right \}\right \}\] ✓ Maple : cpu = 2.059 (sec), leaf count = 50
dsolve(x*y(x)*diff(diff(y(x),x),x)+(a*x/(b^2-x^2)^(1/2)-x)*diff(y(x),x)^2-y(x)*diff(y(x),x)=0,y(x))
\[y \left (x \right ) = c_{2} {\mathrm e}^{\int -\frac {x \sqrt {b^{2}-x^{2}}}{c_{1} \sqrt {b^{2}-x^{2}}+a \left (b^{2}-x^{2}\right )}d x}\]