Internal problem ID [10854]
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 54.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }-x -{\mathrm e}^{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 52
dsolve(diff(y(x),x$6)+2*diff(y(x),x$4)+diff(y(x),x$2)=x+exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}}{6}-c_{1} \cos \left (x \right )-c_{2} \sin \left (x \right )+c_{3} \left (2 \sin \left (x \right )-\cos \left (x \right ) x \right )+c_{4} \left (-\sin \left (x \right ) x -2 \cos \left (x \right )\right )+\frac {{\mathrm e}^{x}}{4}+c_{5} x +c_{6} \]
✓ Solution by Mathematica
Time used: 0.404 (sec). Leaf size: 56
DSolve[y''''''[x]+2*y''''[x]+y''[x]==x+Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{6}+\frac {e^x}{4}+c_6 x-(c_2 x+c_1+2 c_4) \cos (x)-(c_4 x-2 c_2+c_3) \sin (x)+c_5 \\ \end{align*}