2.310   ODE No. 310

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

✓ Mathematica : cpu = 0.128078 (sec), leaf count = 159

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

\[\left \{\left \{y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \}\right \}\]

✓ Maple : cpu = 0.145 (sec), leaf count = 125

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

\[y \left (x \right ) = -\frac {\sqrt {-10 x^{2} c_{1} -2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}}\]