60.5.14 problem 1549

Internal problem ID [11548]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1549
Date solved : Monday, January 27, 2025 at 11:23:23 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-24&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(x*diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x)-24=0,y(x), singsol=all)
 

\[ y = \frac {4 x^{3}}{5}-\frac {c_{1}}{24 x^{2}}+\frac {c_{2} x^{2}}{2}+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 34

DSolve[-24 + 5*Derivative[3][y][x] + x*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 x^3}{5}+c_4 x^2-\frac {c_1}{24 x^2}+c_3 x+c_2 \]