60.5.2 problem 1535

Internal problem ID [11536]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1535
Date solved : Monday, January 27, 2025 at 11:23:16 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y-f&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+4*y(x)-f=0,y(x), singsol=all)
 

\[ y = \frac {f}{4}+\cos \left (x \right ) c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} \sin \left (x \right )+c_3 \,{\mathrm e}^{-x} \cos \left (x \right )+c_4 \sin \left (x \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.161 (sec). Leaf size: 172

DSolve[-f[x] + 4*y[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\cos (x) \int _1^x\frac {1}{8} e^{K[1]} f(K[1]) (\cos (K[1])-\sin (K[1]))dK[1]+e^{2 x} \cos (x) \int _1^x-\frac {1}{8} e^{-K[4]} f(K[4]) (\cos (K[4])+\sin (K[4]))dK[4]+\sin (x) \int _1^x\frac {1}{8} e^{K[2]} f(K[2]) (\cos (K[2])+\sin (K[2]))dK[2]+e^{2 x} \sin (x) \int _1^x\frac {1}{8} e^{-K[3]} f(K[3]) (\cos (K[3])-\sin (K[3]))dK[3]+c_1 \cos (x)+c_4 e^{2 x} \cos (x)+c_2 \sin (x)+c_3 e^{2 x} \sin (x)\right ) \]