60.6.6 problem 1583

Internal problem ID [11582]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 5, linear fifth and higher order
Problem number : 1583
Date solved : Monday, January 27, 2025 at 11:23:42 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 50

dsolve(diff(y(x),x$5)+a*diff(y(x),x$4)-f=0,y(x), singsol=all)
 

\[ y = \frac {6 c_{1} {\mathrm e}^{-a x}+\left (\left (c_{2} x^{3}+3 x^{2} c_3 +6 c_4 x +6 c_5 \right ) a +\frac {f \,x^{4}}{4}\right ) a^{3}}{6 a^{4}} \]

✓ Solution by Mathematica

Time used: 0.137 (sec). Leaf size: 45

DSolve[D[y[x],{x,5}]+a*D[y[x],{x,4}]-f==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 e^{-a x}}{a^4}+\frac {f x^4}{24 a}+x (x (c_5 x+c_4)+c_3)+c_2 \]