Internal problem ID [9906]
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]]
\[ \boxed {y^{\left (5\right )}+a y^{\prime \prime \prime \prime }=f} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(diff(y(x),x$5)+a*diff(y(x),x$4)-f=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {6 \,{\mathrm e}^{-a x} c_{1} +a^{3} \left (\left (c_{2} x^{3}+3 x^{2} c_{3} +6 c_{4} x +6 c_{5} \right ) a +\frac {f \,x^{4}}{4}\right )}{6 a^{4}} \]
✓ Solution by Mathematica
Time used: 0.222 (sec). Leaf size: 45
DSolve[y'''''[x]+a*y''''[x]-f==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 e^{-a x}}{a^4}+\frac {f x^4}{24 a}+x (x (c_5 x+c_4)+c_3)+c_2 \]