2.24   ODE No. 24

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

\[ a y(x)^2-b x^{\nu }+y'(x)=0 \] Mathematica : cpu = 0.0135686 (sec), leaf count = 277

\[\left \{\left \{y(x)\to -\frac {\sqrt {-a} \sqrt {b} x^{\frac {\nu +2}{2}} \left (c_1 J_{\frac {\nu +1}{\nu +2}}\left (\frac {2 \sqrt {-a} \sqrt {b} x^{\frac {\nu }{2}+1}}{\nu +2}\right )-c_1 J_{-\frac {\nu +3}{\nu +2}}\left (\frac {2 \sqrt {-a} \sqrt {b} x^{\frac {\nu +2}{2}}}{\nu +2}\right )-2 J_{\frac {1}{\nu +2}-1}\left (\frac {2 \sqrt {-a} \sqrt {b} x^{\frac {\nu +2}{2}}}{\nu +2}\right )\right )-c_1 J_{-\frac {1}{\nu +2}}\left (\frac {2 \sqrt {-a} \sqrt {b} x^{\frac {\nu +2}{2}}}{\nu +2}\right )}{2 a x \left (c_1 J_{-\frac {1}{\nu +2}}\left (\frac {2 \sqrt {-a} \sqrt {b} x^{\frac {\nu +2}{2}}}{\nu +2}\right )+J_{\frac {1}{\nu +2}}\left (\frac {2 \sqrt {-a} \sqrt {b} x^{\frac {\nu +2}{2}}}{\nu +2}\right )\right )}\right \}\right \}\]

Maple : cpu = 0.067 (sec), leaf count = 216

\[ \left \{ y \left ( x \right ) =-{\frac {1}{ax} \left ( \sqrt {-ab}{x}^{{\frac {\nu }{2}}+1}{{\sl J}_{{\frac {3+\nu }{\nu +2}}}\left (2\,{\frac {\sqrt {-ab}{x}^{\nu /2+1}}{\nu +2}}\right )}{\it \_C1}+{{\sl Y}_{{\frac {3+\nu }{\nu +2}}}\left (2\,{\frac {\sqrt {-ab}{x}^{\nu /2+1}}{\nu +2}}\right )}\sqrt {-ab}{x}^{{\frac {\nu }{2}}+1}-{\it \_C1}\,{{\sl J}_{ \left ( \nu +2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-ab}{x}^{\nu /2+1}}{\nu +2}}\right )}-{{\sl Y}_{ \left ( \nu +2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-ab}{x}^{\nu /2+1}}{\nu +2}}\right )} \right ) \left ( {\it \_C1}\,{{\sl J}_{ \left ( \nu +2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-ab}{x}^{\nu /2+1}}{\nu +2}}\right )}+{{\sl Y}_{ \left ( \nu +2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-ab}{x}^{\nu /2+1}}{\nu +2}}\right )} \right ) ^{-1}} \right \} \]