Internal problem ID [10853]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 53.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\left (6\right )}-y-{\mathrm e}^{2 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 73
dsolve(diff(y(x),x$6)-y(x)=exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x}}{63}+c_{1} {\mathrm e}^{x}+{\mathrm e}^{-x} c_{2} +c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{4} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{5} {\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{6} {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.429 (sec). Leaf size: 80
DSolve[y''''''[x]-y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 x}}{63}+c_1 e^x+c_4 e^{-x}+e^{-x/2} \left (\left (c_2 e^x+c_3\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+\left (c_6 e^x+c_5\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}