7.17 problem Exercise 20.18, page 220

Internal problem ID [4080]

Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.18, page 220.
ODE order: 4.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 20

dsolve(diff(y(x),x$4)+3*diff(y(x),x$3)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1}+c_{2} x +c_{3} x^{2}+c_{4} {\mathrm e}^{-3 x} \]

Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 28

DSolve[y''''[x]+3*y'''[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{27} c_1 e^{-3 x}+x (c_4 x+c_3)+c_2 \\ \end{align*}