Internal problem ID [12202]
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]]
\[ \boxed {y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }=x +{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(diff(y(x),x$6)+2*diff(y(x),x$4)+diff(y(x),x$2)=x+exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-c_{3} x -c_{1} -2 c_{4} \right ) \cos \left (x \right )+\left (-c_{4} x -c_{2} +2 c_{3} \right ) \sin \left (x \right )+\frac {x^{3}}{6}+c_{5} x +c_{6} +\frac {{\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 0.61 (sec). Leaf size: 58
DSolve[y''''''[x]+2*y''''[x]+y''[x]==x+Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{6}+\frac {e^x}{4}+c_6 x-(c_2 x+c_1+2 c_4) \cos (x)+(-c_4 x+2 c_2-c_3) \sin (x)+c_5 \]