2.1676   ODE No. 1676

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

\[ a \left (x y'(x)-y(x)\right )^2-b x^2+x^2 y''(x)=0 \] Mathematica : cpu = 50.8611 (sec), leaf count = 133

\[\left \{\left \{y(x)\to x \left (c_2+\int _1^x \frac {i \sqrt {a} \sqrt {b} Y_1\left (-i \sqrt {a} \sqrt {b} K[2]\right )-i \sqrt {a} \sqrt {b} c_1 J_1\left (i \sqrt {a} \sqrt {b} K[2]\right )}{a K[2] \left (c_1 J_0\left (i \sqrt {a} \sqrt {b} K[2]\right )+Y_0\left (-i \sqrt {a} \sqrt {b} K[2]\right )\right )} \, dK[2]\right )\right \}\right \}\]

Maple : cpu = 0.502 (sec), leaf count = 79

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\, \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) ,[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =-a{\it \_a}\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-2\,{\frac {{\it \_b} \left ( {\it \_a} \right ) }{{\it \_a}}}+{\frac {b}{{\it \_a}}} \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x}}-{\frac {y \left ( x \right ) }{{x}^{2}}} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_a}\, \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \right \} ] \right ) \right \} \]