Internal problem ID [12193]
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 41.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(y(x),x$6)-3*diff(y(x),x$5)+3*diff(y(x),x$4)-diff(y(x),x$3)=x,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{3} x^{2}+\left (c_{2} -6 c_{3} \right ) x +c_{1} -3 c_{2} +12 c_{3} \right ) {\mathrm e}^{x}-\frac {x^{4}}{24}-\frac {x^{3}}{2}+\frac {c_{4} x^{2}}{2}+c_{5} x +c_{6} \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 61
DSolve[y''''''[x]-3*y'''''[x]+3*y''''[x]-y'''[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^4}{24}-\frac {x^3}{2}+c_6 x^2+c_3 e^x \left (x^2-6 x+12\right )+c_5 x+c_1 e^x+c_2 e^x (x-3)+c_4 \]