\[ y''(x)-a \left (y'(x)^2+1\right )^{3/2} (b x+c+y(x))=0 \] ✗ Mathematica : cpu = 100.302 (sec), leaf count = 0 , could not solve
DSolve[-(a*(c + b*x + y[x])*(1 + Derivative[1][y][x]^2)^(3/2)) + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.777 (sec), leaf count = 771
\[ \left \{ y \left ( x \right ) =-bx+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{ \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) \left ( {b}^{2}+1 \right ) b} \left ( 4\,{a}^{2}{b}^{2}{c}^{2}{{\it \_f}}^{2}+4\,{a}^{2}{b}^{2}c{{\it \_f}}^{3}+{a}^{2}{b}^{2}{{\it \_f}}^{4}-8\,{\it \_C1}\,{a}^{2}{b}^{2}c{\it \_f}-4\,{\it \_C1}\,{a}^{2}{b}^{2}{{\it \_f}}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}{b}^{2}-2\,\sqrt {-{b}^{2} \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) }ac{\it \_f}-\sqrt {-{b}^{2} \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) }a{{\it \_f}}^{2}-4\,{b}^{4}+2\,\sqrt {-{b}^{2} \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) }{\it \_C1}\,a-4\,{b}^{2} \right ) }{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-bx+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!-{\frac {1}{ \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) \left ( {b}^{2}+1 \right ) b} \left ( -{a}^{2}{b}^{2}{{\it \_f}}^{4}-4\,{a}^{2}{b}^{2}c{{\it \_f}}^{3}-4\,{a}^{2}{b}^{2}{c}^{2}{{\it \_f}}^{2}+4\,{\it \_C1}\,{a}^{2}{b}^{2}{{\it \_f}}^{2}+8\,{\it \_C1}\,{a}^{2}{b}^{2}c{\it \_f}-4\,{{\it \_C1}}^{2}{a}^{2}{b}^{2}-\sqrt {-{b}^{2} \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) }a{{\it \_f}}^{2}-2\,\sqrt {-{b}^{2} \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) }ac{\it \_f}+4\,{b}^{4}+2\,\sqrt {-{b}^{2} \left ( {{\it \_f}}^{4}{a}^{2}+4\,c{{\it \_f}}^{3}{a}^{2}+4\,{c}^{2}{{\it \_f}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-8\,{\it \_C1}\,c{\it \_f}\,{a}^{2}+4\,{{\it \_C1}}^{2}{a}^{2}-4\,{b}^{2}-4 \right ) }{\it \_C1}\,a+4\,{b}^{2} \right ) }{d{\it \_f}}+{\it \_C2} \right ) \right \} \]