2.297   ODE No. 297

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ 2 x \left (5 x^2+y(x)^2\right ) y'(x)-x^2 y(x)+y(x)^3=0 \] Mathematica : cpu = 0.19034 (sec), leaf count = 216

\[\left \{\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,5\right ]\right \}\right \}\] Maple : cpu = 0.293 (sec), leaf count = 29

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