2.1090   ODE No. 1090

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

\[ a \left (a^2-2 b e^{-a x}\right ) y'(x)+a^2 y''(x)+b^2 e^{-2 a x} y(x)=0 \] Mathematica : cpu = 0.0352361 (sec), leaf count = 50

\[\left \{\left \{y(x)\to c_1 e^{-\frac {b e^{-a x}}{a^2}}-\frac {b c_2 e^{-\frac {b e^{-a x}}{a^2}-a x}}{a^2}\right \}\right \}\]

Maple : cpu = 0.062 (sec), leaf count = 59

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {{a}^{3}x+2\,b{{\rm e}^{-ax}}}{2\,{a}^{2}}}}}\sinh \left ( {\frac {ax}{2}} \right ) +{\it \_C2}\,{{\rm e}^{-{\frac {{a}^{3}x+2\,b{{\rm e}^{-ax}}}{2\,{a}^{2}}}}}\cosh \left ( {\frac {ax}{2}} \right ) \right \} \]