2.1583   ODE No. 1583

\[ a y^{(4)}(x)-f(x)+y^{(5)}(x)=0 \]

✓ Mathematica : cpu = 0.110071 (sec), leaf count = 92

DSolve[-f[x] + a*Derivative[4][y][x] + Derivative[5][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \int _1^x\int _1^{K[5]}\int _1^{K[4]}\int _1^{K[3]}\left (e^{-a K[2]} c_1+e^{-a K[2]} \int _1^{K[2]}e^{a K[1]} f(K[1])dK[1]\right )dK[2]dK[3]dK[4]dK[5]+c_5 x^3+c_4 x^2+c_3 x+c_2\right \}\right \}\]

✓ Maple : cpu = 0.057 (sec), leaf count = 40

dsolve(diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+a*diff(diff(diff(diff(y(x),x),x),x),x)-f=0,y(x))
 

\[y \left (x \right ) = \frac {f \,x^{4}}{24 a}+\frac {c_{3} x^{2}}{2}+\frac {c_{2} x^{3}}{6}+\frac {c_{1} {\mathrm e}^{-a x}}{a^{4}}+c_{4} x +c_{5}\]