Internal problem ID [9114]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1535.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+4 y-f=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 36
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+4*y(x)-f=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {f}{4}+c_{1} {\mathrm e}^{x} \cos \relax (x )+c_{2} {\mathrm e}^{x} \sin \relax (x )+c_{3} {\mathrm e}^{-x} \cos \relax (x )+c_{4} {\mathrm e}^{-x} \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 155
DSolve[-f[x] + 4*y[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (\cos (x) \int _1^x\frac {1}{8} e^{K[1]} f(K[1]) (\cos (K[1])-\sin (K[1]))dK[1]+\sin (x) \int _1^x\frac {1}{8} e^{K[2]} f(K[2]) (\cos (K[2])+\sin (K[2]))dK[2]+e^{2 x} \left (\sin (x) \left (\int _1^x\frac {1}{8} e^{-K[3]} f(K[3]) (\cos (K[3])-\sin (K[3]))dK[3]+c_3\right )+\cos (x) \left (\int _1^x-\frac {1}{8} e^{-K[4]} f(K[4]) (\cos (K[4])+\sin (K[4]))dK[4]+c_4\right )\right )+c_1 \cos (x)+c_2 \sin (x)\right ) \\ \end{align*}