2.147   ODE No. 147

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

\[ a x^2 y(x)^3+b y(x)^2+x^2 y'(x)=0 \] Mathematica : cpu = 0.907638 (sec), leaf count = 279

\[\text {Solve}\left [\frac {\frac {(b y(x)+x) \text {Ai}\left (\frac {x^2+2 b y(x) x+\left (b^2-2 a x^3\right ) y(x)^2}{2 \sqrt [3]{2} a^{2/3} b^{2/3} x^2 y(x)^2}\right )}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} x y(x)}+\text {Ai}'\left (\frac {x^2+2 b y(x) x+\left (b^2-2 a x^3\right ) y(x)^2}{2 \sqrt [3]{2} a^{2/3} b^{2/3} x^2 y(x)^2}\right )}{\frac {(b y(x)+x) \text {Bi}\left (\frac {x^2+2 b y(x) x+\left (b^2-2 a x^3\right ) y(x)^2}{2 \sqrt [3]{2} a^{2/3} b^{2/3} x^2 y(x)^2}\right )}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} x y(x)}+\text {Bi}'\left (\frac {x^2+2 b y(x) x+\left (b^2-2 a x^3\right ) y(x)^2}{2 \sqrt [3]{2} a^{2/3} b^{2/3} x^2 y(x)^2}\right )}+c_1=0,y(x)\right ]\]

Maple : cpu = 0.215 (sec), leaf count = 178

\[ \left \{ y \left ( x \right ) =-{\sqrt [3]{2}abx \left ( \sqrt [3]{2}a{b}^{2}-2\, \left ( {a}^{2}{b}^{2} \right ) ^{2/3}{\it RootOf} \left ( {{\rm Bi}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )}{\it \_C1}\,{\it \_Z}+{\it \_Z}\,{{\rm Ai}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )}+{{\rm Bi}^{(1)}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )}{\it \_C1}+{{\rm Ai}^{(1)}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )} \right ) x \right ) ^{-1}} \right \} \]