7.18 problem Exercise 20.19, page 220

Internal problem ID [4081]

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 20.19, 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 }-2 y^{\prime \prime }=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)-2*diff(y(x),x$2)=0,y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 42

DSolve[y''''[x]-2*y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} e^{-\sqrt {2} x} \left (c_1 e^{2 \sqrt {2} x}+c_2\right )+c_4 x+c_3 \\ \end{align*}