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: 1579.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\relax (5)}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \relax (x )-c \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 78
dsolve(diff(y(x),x$5)+2*diff(y(x),x$3)+diff(y(x),x)-a*x-b*sin(x)-c*cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {a \,x^{2}}{2}+c_{1} \sin \relax (x )-c_{2} \cos \relax (x )+\sin \relax (x ) c_{3} x +\cos \relax (x ) c_{3}-\cos \relax (x ) c_{4} x +c_{4} \sin \relax (x )-\frac {3 b \cos \relax (x )}{4}+\frac {3 \sin \relax (x ) c}{4}-\frac {b \sin \relax (x ) x}{2}-\frac {\cos \relax (x ) c x}{2}-\frac {\sin \relax (x ) c \,x^{2}}{8}+\frac {\cos \relax (x ) b \,x^{2}}{8}+c_{5} \]
✓ Solution by Mathematica
Time used: 0.565 (sec). Leaf size: 79
DSolve[y'''''[x]+2*y'''[x]+y'[x]-a*x-b*Sin[x]-c*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a x^2}{2}+\cos (x) \left (\frac {1}{16} b \left (2 x^2-9\right )-\frac {5 c x}{8}-c_4 x+c_2-c_3\right )+\sin (x) \left (-\frac {3 b x}{8}+\frac {1}{16} c \left (13-2 x^2\right )+c_2 x+c_1+c_4\right )+c_5 \\ \end{align*}