6.6 problem 1583

Internal problem ID [9158]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1583.
ODE order: 5.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _missing_x]]

\[ \boxed {y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 40

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

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

Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 45

DSolve[y'''''[x]+a*y''''[x]-f==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} 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 \\ \end{align*}