\[ x^2+4 x y'(x)+3 y'(x)^2-y(x)=0 \] ✓ Mathematica : cpu = 5.44897 (sec), leaf count = 1211
DSolve[x^2 - y[x] + 4*x*Derivative[1][y][x] + 3*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {1}{2} \left (\frac {\tanh ^{-1}\left (\frac {1-3 x}{2 \sqrt {1-9 y(x)}}\right )}{\sqrt {1-9 y(x)}}+\log \left (-3 x^2+2 x-12 y(x)+1\right )+\frac {9 \tanh ^{-1}\left (\frac {-2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right ) y(x)}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5}}-\frac {9 \tanh ^{-1}\left (\frac {2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right ) y(x)}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5}}+\frac {\tanh ^{-1}\left (\frac {3 x-1}{2 \sqrt {1-9 y(x)}}\right )}{\sqrt {1-9 y(x)}}+\frac {2 \tanh ^{-1}\left (\frac {-2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5}}-\frac {\tanh ^{-1}\left (\frac {-2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5}}+\frac {2 \tanh ^{-1}\left (\frac {2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5}}+\frac {\tanh ^{-1}\left (\frac {2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5}}\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{2} \left (\frac {\tanh ^{-1}\left (\frac {1-3 x}{2 \sqrt {1-9 y(x)}}\right )}{\sqrt {1-9 y(x)}}+\log \left (-3 x^2+2 x-12 y(x)+1\right )-\frac {9 \tanh ^{-1}\left (\frac {-2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right ) y(x)}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5}}+\frac {9 \tanh ^{-1}\left (\frac {2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right ) y(x)}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5}}+\frac {\tanh ^{-1}\left (\frac {3 x-1}{2 \sqrt {1-9 y(x)}}\right )}{\sqrt {1-9 y(x)}}-\frac {2 \tanh ^{-1}\left (\frac {-2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5}}+\frac {\tanh ^{-1}\left (\frac {-2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)-4 \sqrt {1-9 y(x)}+5}}-\frac {2 \tanh ^{-1}\left (\frac {2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5}}-\frac {\tanh ^{-1}\left (\frac {2 \sqrt {1-9 y(x)} x+x+9 y(x)}{\sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5} \sqrt {x^2+3 y(x)}}\right )}{\sqrt {1-9 y(x)} \sqrt {-9 y(x)+4 \sqrt {1-9 y(x)}+5}}\right )=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.156 (sec), leaf count = 101
dsolve(3*diff(y(x),x)^2+4*x*diff(y(x),x)-y(x)+x^2 = 0,y(x))
\[y \left (x \right ) = -\frac {x^{2}}{3}\]