2.1576   ODE No. 1576

\[ 2 f'(x) \left (y^{(3)}(x)-a^2 y'(x)\right )+f(x) \left (a^4 y(x)-2 a^2 y''(x)+y^{(4)}(x)\right )=0 \]

✗ Mathematica : cpu = 0.1746 (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))
 

\[y \left (x \right ) = {\mathrm e}^{-a x} c_{1} +c_{2} {\mathrm e}^{a x}+c_{3} {\mathrm e}^{\frac {\left (-\operatorname {df} +\sqrt {a^{2} f^{2}+\operatorname {df}^{2}}\right ) x}{f}}+c_{4} {\mathrm e}^{-\frac {\left (\operatorname {df} +\sqrt {a^{2} f^{2}+\operatorname {df}^{2}}\right ) x}{f}}\]