\[ a y(x)^3+b y(x)^2+c y(x)+4 y(x) y''(x)-3 y'(x)^2=0 \] ✓ Mathematica : cpu = 0.593348 (sec), leaf count = 107
DSolve[c*y[x] + b*y[x]^2 + a*y[x]^3 - 3*Derivative[1][y][x]^2 + 4*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {1}{\sqrt {-\frac {1}{3} a K[1]^3-b K[1]^2+c_1 K[1]^{3/2}+c K[1]}}dK[1]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sqrt {-\frac {1}{3} a K[2]^3-b K[2]^2+c_1 K[2]^{3/2}+c K[2]}}dK[2]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.032 (sec), leaf count = 87
dsolve(4*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+a*y(x)^3+b*y(x)^2+y(x)*c=0,y(x))
\[y \left (x \right ) = 0\]