6.5   ODE No. 1538

$$\boxed{{\displaystyle \mathit{d}\mathit{4}\mathit{y}\left(x\right)+2a^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+a^{4}y\left(x\right)-\cosh \left(ax\right)=0}}$$

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

Mathematica: cpu = 0.247531 (sec), leaf count = 66 $$\left\{\{y(x)\to \frac{{\cos }^2(ax)\cosh (ax)+{\sin }^2(ax)\cosh (ax)}{4a^4}+c_3\sin (ax)+c_{4}x\sin (ax)+c_1\cos (ax)+c_{2}x\cos (ax)\}\right\}$$

Maple: cpu = 0.250 (sec), leaf count = 46 $$\{y\left(x\right)=\frac{{\mathrm{e}}^{ax}+{\mathrm{e}}^{-ax}}{8a^4}+\mathit{\_}\mathit{C}\mathit{1}\cos \left(ax\right)+\mathit{\_}\mathit{C}\mathit{2}\sin \left(ax\right)+\mathit{\_}\mathit{C}\mathit{3}\cos \left(ax\right)x+\mathit{\_}\mathit{C}\mathit{4}\sin \left(ax\right)x\}$$