2.298   ODE No. 298

\[ 3 x y(x)^2 y'(x)+y(x)^3-2 x=0 \]

✓ Mathematica : cpu = 0.0725767 (sec), leaf count = 72

DSolve[-2*x + y[x]^3 + 3*x*y[x]^2*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {\sqrt [3]{x^2+c_1}}{\sqrt [3]{x}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}}\right \}\right \}\]

✓ Maple : cpu = 0.031 (sec), leaf count = 73

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

\[y \left (x \right ) = \frac {{\left (\left (x^{2}+c_{1} \right ) x^{2}\right )}^{{1}/{3}}}{x}\]