\[ y'(x)=-\frac {\sqrt {a} \left (-2 \sqrt {a x^4+8 y(x)}+\sqrt {a} x^4+\sqrt {a} x^3\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.43991 (sec), leaf count = 41
DSolve[Derivative[1][y][x] == -1/2*(Sqrt[a]*(Sqrt[a]*x^3 + Sqrt[a]*x^4 - 2*Sqrt[a*x^4 + 8*y[x]]))/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{8} \left (-a x^4+16 a \log ^2(x+1)-32 a c_1 \log (x+1)+16 a c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.669 (sec), leaf count = 28
dsolve(diff(y(x),x) = -1/2*(a^(1/2)*x^4+a^(1/2)*x^3-2*(a*x^4+8*y(x))^(1/2))*a^(1/2)/(1+x),y(x))
\[-\frac {\sqrt {a \,x^{4}+8 y \left (x \right )}}{4 \sqrt {a}}+\ln \left (1+x \right )-c_{1} = 0\]