2.313 ODE No. 313
\[ y'(x) \left (3 a x y(x)^2+2 a y(x)^3-b x^3+c x^2\right )-a y(x)^3+2 b x^3+3 b x^2 y(x)+c y(x)^2=0 \]
✓ Mathematica : cpu = 0.280999 (sec), leaf count = 537
DSolve[2*b*x^3 + 3*b*x^2*y[x] + c*y[x]^2 - a*y[x]^3 + (c*x^2 - b*x^3 + 3*a*x*y[x]^2 + 2*a*y[x]^3)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{2} (3 a c x+3 a c_1)}{3 a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}-\frac {\sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{3 \sqrt [3]{2} a}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{6 \sqrt [3]{2} a}-\frac {\left (1+i \sqrt {3}\right ) (3 a c x+3 a c_1)}{3\ 2^{2/3} a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{6 \sqrt [3]{2} a}-\frac {\left (1-i \sqrt {3}\right ) (3 a c x+3 a c_1)}{3\ 2^{2/3} a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}\right \}\right \}\]
✓ Maple : cpu = 0.273 (sec), leaf count = 748
dsolve((2*a*y(x)^3+3*a*x*y(x)^2-b*x^3+c*x^2)*diff(y(x),x)-a*y(x)^3+c*y(x)^2+3*b*y(x)*x^2+2*b*x^3 = 0,y(x))
\[y \left (x \right ) = \frac {\left (-12 c x +12 c_{1} \right ) a +{\left (\left (-108 b \,x^{3}+108 x c_{1} +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 a b c_{1} x^{4}+12 c^{3} x^{3}+81 a \,c_{1}^{2} x^{2}-36 c^{2} c_{1} x^{2}+36 c \,c_{1}^{2} x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )}^{{2}/{3}}}{6 {\left (\left (-108 b \,x^{3}+108 x c_{1} +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 a b c_{1} x^{4}+12 c^{3} x^{3}+81 a \,c_{1}^{2} x^{2}-36 c^{2} c_{1} x^{2}+36 c \,c_{1}^{2} x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )}^{{1}/{3}} a}\]