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 = 3.12605 (sec), leaf count = 13289 \[ \text {Too large to display} \] Maple : cpu = 0.408 (sec), leaf count = 160

\[ \left \{ y \left ( x \right ) ={\frac {x \left ( {\it \_C1}\,x-b{\it RootOf} \left ( {b}^{2}{{\it \_Z}}^{4}-2\,bx{\it \_C1}\,{{\it \_Z}}^{3}+ \left ( {a}^{2}{x}^{2}{{\it \_C1}}^{2}+{b}^{2}{x}^{2}{{\it \_C1}}^{2}+{{\it \_C1}}^{2}{x}^{2}-{a}^{2} \right ) {{\it \_Z}}^{2}-2\,b{x}^{3}{{\it \_C1}}^{3}{\it \_Z}+{x}^{4}{{\it \_C1}}^{4} \right ) \right ) }{a{\it RootOf} \left ( {b}^{2}{{\it \_Z}}^{4}-2\,bx{\it \_C1}\,{{\it \_Z}}^{3}+ \left ( {a}^{2}{x}^{2}{{\it \_C1}}^{2}+{b}^{2}{x}^{2}{{\it \_C1}}^{2}+{{\it \_C1}}^{2}{x}^{2}-{a}^{2} \right ) {{\it \_Z}}^{2}-2\,b{x}^{3}{{\it \_C1}}^{3}{\it \_Z}+{x}^{4}{{\it \_C1}}^{4} \right ) }} \right \} \]