Internal problem ID [9155]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1580.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 80
dsolve(diff(y(x),x$6)+y(x)-sin(3/2*x)*sin(1/2*x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\cos \left (2 x \right )}{126}+\frac {x \sin \left (x \right )}{12}+\frac {\cos \left (x \right )}{9}+c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )+c_{3} {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}} \cos \left (\frac {x}{2}\right )+c_{4} {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}} \sin \left (\frac {x}{2}\right )+c_{5} {\mathrm e}^{\frac {\sqrt {3}\, x}{2}} \cos \left (\frac {x}{2}\right )+c_{6} {\mathrm e}^{\frac {\sqrt {3}\, x}{2}} \sin \left (\frac {x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 4.114 (sec). Leaf size: 93
DSolve[y''''''[x]+y[x]-Sin[3/2*x]*Sin[1/2*x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} x \sin (x)+\frac {1}{126} \cos (2 x)+\left (\frac {1}{4}+c_2\right ) \cos (x)+c_5 \sin (x)+e^{-\frac {\sqrt {3} x}{2}} \left (\left (c_1 e^{\sqrt {3} x}+c_3\right ) \cos \left (\frac {x}{2}\right )+\left (c_6 e^{\sqrt {3} x}+c_4\right ) \sin \left (\frac {x}{2}\right )\right ) \\ \end{align*}