20.6.8 problem Problem 30

Internal problem ID [3703]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 30
Date solved : Monday, January 27, 2025 at 07:55:39 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(diff(y(x),x$3)-diff(y(x),x$2)-2*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 28

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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