2.1090   ODE No. 1090

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

$$a(a^2-2b{e}^{-ax})y^{\prime }(x)+a^2{y}^{″}(x)+b^2{e}^{-2ax}y(x)=0$$ ✓ Mathematica : cpu = 0.0343653 (sec), leaf count = 50

$$\left\{\{y(x)\to c_1{e}^{-\frac{b{e}^{-ax}}{a^2}}-\frac{b{c}_2{e}^{-\frac{b{e}^{-ax}}{a^2}-ax}}{a^2}\}\right\}$$

✓ Maple : cpu = 0.048 (sec), leaf count = 59

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{a^{3}x+2b{\mathrm{e}}^{-ax}}{2a^2}}\sinh \left(\frac{ax}{2}\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{a^{3}x+2b{\mathrm{e}}^{-ax}}{2a^2}}\cosh \left(\frac{ax}{2}\right)\}$$