Internal problem ID [11749]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 19.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(diff(y(x),x$5)-2*diff(y(x),x$4)+diff(y(x),x$3)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{5} x +c_{4} \right ) {\mathrm e}^{x}+c_{3} x^{2}+c_{2} x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 30
DSolve[y'''''[x]-2*y''''[x]+y'''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (c_2 (x-3)+c_1)+x (c_5 x+c_4)+c_3 \]