2.326   ODE No. 326

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

\[ y(x) y'(x) \left ((a y(x)+b x)^3+b x^3\right )+x \left ((a y(x)+b x)^3+a y(x)^3\right )=0 \] Mathematica : cpu = 3.45581 (sec), leaf count = 13289 \[ \text {Too large to display} \] Maple : cpu = 0.537 (sec), leaf count = 160

\[\left \{y \left (x \right ) = \frac {\left (c_{1} x -b \RootOf \left (c_{1}^{4} x^{4}-2 c_{1}^{3} \textit {\_Z} b \,x^{3}-2 c_{1} \textit {\_Z}^{3} b x +\textit {\_Z}^{4} b^{2}+\left (a^{2} x^{2} c_{1}^{2}+b^{2} x^{2} c_{1}^{2}+c_{1}^{2} x^{2}-a^{2}\right ) \textit {\_Z}^{2}\right )\right ) x}{a \RootOf \left (c_{1}^{4} x^{4}-2 c_{1}^{3} \textit {\_Z} b \,x^{3}-2 c_{1} \textit {\_Z}^{3} b x +\textit {\_Z}^{4} b^{2}+\left (a^{2} x^{2} c_{1}^{2}+b^{2} x^{2} c_{1}^{2}+c_{1}^{2} x^{2}-a^{2}\right ) \textit {\_Z}^{2}\right )}\right \}\]