2.1576   ODE No. 1576

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

$$2f^{\prime }(x)(y^{(3)}(x)-a^2{y}^{\prime }(x))+f(x)(a^{4}y(x)-2a^2{y}^{″}(x)+y^{(4)}(x))=0$$ ✗ Mathematica : cpu = 0.249435 (sec), leaf count = 0 , could not solve

DSolve[2*Derivative[1][f][x]*(-(a^2*Derivative[1][y][x]) + Derivative[3][y][x]) + f[x]*(a^4*y[x] - 2*a^2*Derivative[2][y][x] + Derivative[4][y][x]) == 0, y[x], x]

✓ Maple : cpu = 0.032 (sec), leaf count = 67

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