\[ (y(x)-x)^2 \left (y'(x)^2+1\right )-a^2 \left (y'(x)+1\right )^2=0 \] ✓ Mathematica : cpu = 20.5772 (sec), leaf count = 17831
DSolve[-(a^2*(1 + Derivative[1][y][x])^2) + (-x + y[x])^2*(1 + Derivative[1][y][x]^2) == 0,y[x],x]
\[ \text {Too large to display} \] ✓ Maple : cpu = 0.256 (sec), leaf count = 130
dsolve((y(x)-x)^2*(diff(y(x),x)^2+1)-a^2*(diff(y(x),x)+1)^2 = 0,y(x))
\[y \left (x \right ) = x -\sqrt {2}\, a\]