2.1204   ODE No. 1204

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

\[ x^2 (a+2 b) y'(x)+y(x) \left (b x^2 (a+b)-2\right )+x^2 y''(x)=0 \] Mathematica : cpu = 0.0176808 (sec), leaf count = 132

\[\left \{\left \{y(x)\to \frac {2 c_2 e^{\frac {1}{2} (-a x-2 b x+\log (x))} \left (i \sinh \left (\frac {a x}{2}\right )-\frac {2 i \cosh \left (\frac {a x}{2}\right )}{a x}\right )}{\sqrt {\pi } \sqrt {-i a x}}+\frac {2 c_1 e^{\frac {1}{2} (-a x-2 b x+\log (x))} \left (\frac {2 \sinh \left (\frac {a x}{2}\right )}{a x}-\cosh \left (\frac {a x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i a x}}\right \}\right \}\] Maple : cpu = 0.094 (sec), leaf count = 35

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\, \left ( ax+2 \right ) {{\rm e}^{- \left ( a+b \right ) x}}+{\it \_C1}\,{{\rm e}^{-bx}} \left ( ax-2 \right ) }{x}} \right \} \]