ODE No. 285

$$(3x^2+2xy(x)+4y(x{)}^2)y^{\prime }(x)+2x^2+6xy(x)+y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.167262 (sec), leaf count = 402

DSolve[2*x^2 + 6*x*y[x] + y[x]^2 + (3*x^2 + 2*x*y[x] + 4*y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
 

$$\{\{y(x)\to \frac{\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}{12\sqrt[3]{2}}-\frac{33x^2}{22^{2/3}\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}-\frac{x}{4}\},\{y(x)\to -\frac{(1-i\sqrt{3})\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}{24\sqrt[3]{2}}+\frac{33(1+i\sqrt{3})x^2}{42^{2/3}\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}-\frac{x}{4}\},\{y(x)\to -\frac{(1+i\sqrt{3})\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}{24\sqrt[3]{2}}+\frac{33(1-i\sqrt{3})x^2}{42^{2/3}\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}-\frac{x}{4}\}\}$$ ✓ Maple : cpu = 0.077 (sec), leaf count = 432

dsolve((4*y(x)^2+2*x*y(x)+3*x^2)*diff(y(x),x)+y(x)^2+6*x*y(x)+2*x^2 = 0,y(x))
 

$$y\left(x\right)=\frac{\frac{{(x^3{c}_1^3+8+2\sqrt{333x^6{c}_1^6+4x^3{c}_1^3+16})}^{\frac{1}{3}}}{4}-\frac{11c_1^2{x}^2}{4{(x^3{c}_1^3+8+2\sqrt{333x^6{c}_1^6+4x^3{c}_1^3+16})}^{\frac{1}{3}}}-\frac{c_{1}x}{4}}{c_1}$$