\[ (a y(x)-b x)^2 \left (a^2 y'(x)^2+b^2\right )-c^2 \left (a y'(x)+b\right )^2=0 \] ✓ Mathematica : cpu = 1.27299 (sec), leaf count = 100
\[\left \{\left \{y(x)\to \frac {b c_1}{a}-\frac {\sqrt {b^2 \left (-x^2\right )+2 b^2 c_1 x-b^2 c_1{}^2+c^2}}{a}\right \},\left \{y(x)\to \frac {\sqrt {b^2 \left (-x^2\right )+2 b^2 c_1 x-b^2 c_1{}^2+c^2}}{a}+\frac {b c_1}{a}\right \}\right \}\] ✓ Maple : cpu = 0.354 (sec), leaf count = 195
\[\left \{y \left (x \right ) = \frac {a \RootOf \left (c_{1}-x +\int _{}^{\textit {\_Z}}\frac {\left (-\textit {\_a}^{2} a^{2}+2 c^{2}+\sqrt {-\left (\textit {\_a}^{2} a^{2}-2 c^{2}\right ) \textit {\_a}^{2} a^{2}}\right ) a}{2 \left (\textit {\_a}^{2} a^{2}-2 c^{2}\right ) b}d \textit {\_a} \right )+b x}{a}, y \left (x \right ) = \frac {a \RootOf \left (c_{1}-x +\int _{}^{\textit {\_Z}}-\frac {\left (\textit {\_a}^{2} a^{2}-2 c^{2}+\sqrt {-\left (\textit {\_a}^{2} a^{2}-2 c^{2}\right ) \textit {\_a}^{2} a^{2}}\right ) a}{2 \left (\textit {\_a}^{2} a^{2}-2 c^{2}\right ) b}d \textit {\_a} \right )+b x}{a}, y \left (x \right ) = \frac {b x -\sqrt {2}\, c}{a}, y \left (x \right ) = \frac {b x +\sqrt {2}\, c}{a}\right \}\]