32.7.18 problem Exercise 20.19, page 220

Internal problem ID [5933]
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
Date solved : Monday, January 27, 2025 at 01:27:42 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

\[ y \left (x \right ) = c_{1} +c_{2} x +c_3 \,{\mathrm e}^{\sqrt {2}\, x}+c_4 \,{\mathrm e}^{-\sqrt {2}\, x} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 42

DSolve[D[y[x],{x,4}]-2*D[y[x],{x,2}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-\sqrt {2} x} \left (c_1 e^{2 \sqrt {2} x}+c_2\right )+c_4 x+c_3 \]