2.1090   ODE No. 1090

\[ a \left (a^2-2 b e^{-a x}\right ) y'(x)+a^2 y''(x)+b^2 e^{-2 a x} y(x)=0 \]

✓ Mathematica : cpu = 0.027799 (sec), leaf count = 50

DSolve[(b^2*y[x])/E^(2*a*x) + a*(a^2 - (2*b)/E^(a*x))*Derivative[1][y][x] + a^2*Derivative[2][y][x] == 0,y[x],x]
 

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

✓ Maple : cpu = 0.059 (sec), leaf count = 40

dsolve(a^2*diff(diff(y(x),x),x)+a*(a^2-2*b*exp(-a*x))*diff(y(x),x)+b^2*exp(-2*a*x)*y(x)=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{-\frac {a^{3} x +2 b \,{\mathrm e}^{-a x}}{2 a^{2}}} \left (\cosh \left (\frac {a x}{2}\right ) c_{2} +\sinh \left (\frac {a x}{2}\right ) c_{1} \right )\]