Internal problem ID [9903]
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]]
\[ \boxed {y^{\left (6\right )}+y=\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 71
dsolve(diff(y(x),x$6)+y(x)-sin(3/2*x)*sin(1/2*x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\sin \left (\frac {x}{2}\right ) c_{4} +\cos \left (\frac {x}{2}\right ) c_{3} \right ) {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}}+\left (\sin \left (\frac {x}{2}\right ) c_{6} +c_{5} \cos \left (\frac {x}{2}\right )\right ) {\mathrm e}^{\frac {\sqrt {3}\, x}{2}}+\frac {\cos \left (2 x \right )}{126}+\frac {\left (5+24 c_{1} \right ) \cos \left (x \right )}{24}+\frac {\sin \left (x \right ) \left (x +12 c_{2} \right )}{12} \]
✓ Solution by Mathematica
Time used: 6.632 (sec). Leaf size: 111
DSolve[y''''''[x]+y[x]-Sin[3/2*x]*Sin[1/2*x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} x \sin (x)+\frac {1}{126} \cos (2 x)+e^{-\frac {\sqrt {3} x}{2}} \left (c_1 e^{\sqrt {3} x}+c_3\right ) \cos \left (\frac {x}{2}\right )+\left (\frac {1}{4}+c_2\right ) \cos (x)+c_4 e^{-\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_6 e^{\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_5 \sin (x) \]