ODE No. 297

\[ 2 x \left (5 x^2+y(x)^2\right ) y'(x)-x^2 y(x)+y(x)^3=0 \] Mathematica : cpu = 0.163946 (sec), leaf count = 216

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

\[\left \{\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,5\right ]\right \}\right \}\] Maple : cpu = 0.288 (sec), leaf count = 29

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

\[y \left (x \right ) = \RootOf \left (\textit {\_Z}^{45} x^{9} c_{1}-\textit {\_Z}^{18}-6 \textit {\_Z}^{9}-9\right )^{\frac {9}{2}} x\]