3.297   ODE No. 297

\[ \boxed { 2\,x \left ( \left ( y \left ( x \right ) \right ) ^{2}+5\,{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{3}-{x}^{2}y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.058007 (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 = 0.219 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) = \left ( {\it RootOf} \left ( {x}^{9}{\it \_C1}\,{{\it \_Z}}^{45}-{{\it \_Z}}^{18}-6\,{{\it \_Z}}^{9}-9 \right ) \right ) ^{{\frac {9}{2}}}x \right \} \]