2.304   ODE No. 304

$$5x^{2}y(x{)}^3+(10x^{3}y(x{)}^2+x^{2}y(x)+2x)y^{\prime }(x)+xy(x{)}^2=0$$

✓ Mathematica : cpu = 0.268988 (sec), leaf count = 44

DSolve[x*y[x]^2 + 5*x^2*y[x]^3 + (2*x + x^2*y[x] + 10*x^3*y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
 

$$\text{Solve}[y(x)\sqrt{5x^{2}y(x{)}^2+2}{e}^{\frac{{\tan }^{-1}(\sqrt{\frac{5}{2}}xy(x))}{\sqrt{10}}}=c_1,y(x)]$$

✓ Maple : cpu = 0.348 (sec), leaf count = 44

dsolve((10*x^3*y(x)^2+x^2*y(x)+2*x)*diff(y(x),x)+5*x^2*y(x)^3+x*y(x)^2 = 0,y(x))
 

$$y\left(x\right)=\frac{\tan \left(\mathrm{RootOf}(\sqrt{10}\ln \left(\frac{4\tan {\left(\mathit{\text{\_Z}}\right)}^2(\tan {\left(\mathit{\text{\_Z}}\right)}^2+1)}{5x^2}\right)+2\sqrt{10}{c}_1+2\mathit{\text{\_Z}})\right)\sqrt{10}}{5x}$$