2.1538   ODE No. 1538

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

$$2a^2{y}^{″}(x)+a^{4}y(x)-\cosh (ax)+y^{(4)}(x)=0$$ ✓ Mathematica : cpu = 0.159916 (sec), leaf count = 66

$$\left\{\{y(x)\to \frac{{\cos }^2(ax)\cosh (ax)+{\sin }^2(ax)\cosh (ax)}{4a^4}+c_1\cos (ax)+c_{2}x\cos (ax)+c_3\sin (ax)+c_{4}x\sin (ax)\}\right\}$$ ✓ Maple : cpu = 0.371 (sec), leaf count = 49

$$\{y\left(x\right)=\frac{(1+{\mathrm{e}}^{2ax}){\mathrm{e}}^{-ax}+8a^4((\mathit{\_}\mathit{C}\mathit{3}x+\mathit{\_}\mathit{C}\mathit{1})\cos \left(ax\right)+\sin \left(ax\right)(\mathit{\_}\mathit{C}\mathit{4}x+\mathit{\_}\mathit{C}\mathit{2}))}{8a^4}\}$$