2.304   ODE No. 304

\[ 5 x^2 y(x)^3+\left (10 x^3 y(x)^2+x^2 y(x)+2 x\right ) y'(x)+x y(x)^2=0 \]

✓ 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]
 

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

✓ 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))
 

\[y \left (x \right ) = \frac {\tan \left (\operatorname {RootOf}\left (\sqrt {10}\, \ln \left (\frac {4 \tan \left (\textit {\_Z} \right )^{2} \left (\tan \left (\textit {\_Z} \right )^{2}+1\right )}{5 x^{2}}\right )+2 \sqrt {10}\, c_{1} +2 \textit {\_Z} \right )\right ) \sqrt {10}}{5 x}\]