\[ (a y(x)-b x)^2 \left (a^2 y'(x)^2+b^2\right )-c^2 \left (a y'(x)+b\right )^2=0 \] ✓ Mathematica : cpu = 1.09134 (sec), leaf count = 100
DSolve[-(c^2*(b + a*Derivative[1][y][x])^2) + (-(b*x) + a*y[x])^2*(b^2 + a^2*Derivative[1][y][x]^2) == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {b c_1}{a}-\frac {\sqrt {b^2 \left (-x^2\right )+2 b^2 c_1 x-b^2 c_1{}^2+c^2}}{a}\right \},\left \{y(x)\to \frac {\sqrt {b^2 \left (-x^2\right )+2 b^2 c_1 x-b^2 c_1{}^2+c^2}}{a}+\frac {b c_1}{a}\right \}\right \}\] ✓ Maple : cpu = 0.371 (sec), leaf count = 195
dsolve((a*y(x)-b*x)^2*(a^2*diff(y(x),x)^2+b^2)-c^2*(a*diff(y(x),x)+b)^2=0,y(x))
\[y \left (x \right ) = \frac {b x -\sqrt {2}\, c}{a}\]