7.3   ODE No. 1576

$$\boxed{{\displaystyle f(\mathit{d}\mathit{4}\mathit{y}\left(x\right)-2a^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+a^{4}y\left(x\right))+2\mathit{d}\mathit{f}(\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-a^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right))=0}}$$

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

Mathematica: cpu = 0.246031 (sec), leaf count = 50 $$\text{DSolve}[2f^{\prime }(x)(y^{(3)}(x)-a^2{y}^{\prime }(x))+f(x)(a^{4}y(x)-2a^2{y}^{″}(x)+y^{(4)}(x))=0,y(x),x]$$

Maple: cpu = 0.016 (sec), leaf count = 67 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{ax}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-ax}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{x}{f}(-\mathit{d}\mathit{f}+\sqrt{a^2{f}^2+{\mathit{d}\mathit{f}}^2})}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-\frac{x}{f}(\mathit{d}\mathit{f}+\sqrt{a^2{f}^2+{\mathit{d}\mathit{f}}^2})}\}$$