ODE No. 1576

$$2f^{\prime }(x)(y^{(3)}(x)-a^2{y}^{\prime }(x))+f(x)(a^{4}y(x)-2a^2{y}^{″}(x)+y^{(4)}(x))=0$$ ✗ Mathematica : cpu = 0.159509 (sec), leaf count = 0

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]
 

, 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 = 0.02 (sec), leaf count = 67

dsolve(f*(diff(diff(diff(diff(y(x),x),x),x),x)-2*a^2*diff(diff(y(x),x),x)+a^4*y(x))+2*df*(diff(diff(diff(y(x),x),x),x)-a^2*diff(y(x),x))=0,y(x))
 

$$y\left(x\right)=c_1{\mathrm{e}}^{-ax}+c_2{\mathrm{e}}^{ax}+c_3{\mathrm{e}}^{\frac{(-\mathit{df}+\sqrt{a^2{f}^2+{\mathit{df}}^2})x}{f}}+c_4{\mathrm{e}}^{-\frac{(\mathit{df}+\sqrt{a^2{f}^2+{\mathit{df}}^2})x}{f}}$$