#### 2.325   ODE No. 325

$y(x) \left (y(x)^3-2 x^3\right ) y'(x)+x \left (2 y(x)^3-x^3\right )=0$ Mathematica : cpu = 0.190086 (sec), leaf count = 139

$\text {Solve}\left [\frac {1}{7} \text {RootSum}\left [\text {\#1}^4+\text {\#1}^3+3 \text {\#1}^2+\text {\#1}+1\& ,\frac {8 \text {\#1}^3 \log \left (\frac {y(x)}{x}-\text {\#1}\right )+9 \text {\#1}^2 \log \left (\frac {y(x)}{x}-\text {\#1}\right )+12 \text {\#1} \log \left (\frac {y(x)}{x}-\text {\#1}\right )-\log \left (\frac {y(x)}{x}-\text {\#1}\right )}{4 \text {\#1}^3+3 \text {\#1}^2+6 \text {\#1}+1}\& \right ]-\frac {1}{7} \log \left (1-\frac {y(x)}{x}\right )=c_1-\log (x),y(x)\right ]$ Maple : cpu = 0.469 (sec), leaf count = 124

$\left \{ {\frac {1}{7}\ln \left ( {\frac {y \left ( x \right ) -x}{x}} \right ) }-{\frac {2}{7}\ln \left ( {\frac {4\,{x}^{4}+4\,{x}^{3}y \left ( x \right ) +12\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+4\,x \left ( y \left ( x \right ) \right ) ^{3}+4\, \left ( y \left ( x \right ) \right ) ^{4}}{{x}^{4}}} \right ) }-{\frac {2\,\sqrt {3}}{7}\arctan \left ( {\frac {\sqrt {3} \left ( x+2\,y \left ( x \right ) \right ) }{3\,x}} \right ) }+{\frac {2\,\sqrt {3}}{7}\arctan \left ( {\frac {\sqrt {3} \left ( {x}^{3}+4\,{x}^{2}y \left ( x \right ) +2\,x \left ( y \left ( x \right ) \right ) ^{2}+2\, \left ( y \left ( x \right ) \right ) ^{3} \right ) }{3\,{x}^{3}}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0 \right \}$