49.7.3 problem 4(c)

Internal problem ID [7642]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(c)
Date solved : Monday, January 27, 2025 at 03:08:55 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(x),x$3)-5*diff(y(x),x$2)+6*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +{\mathrm e}^{2 x} c_{2} +c_3 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]-5*D[y[x],{x,2}]+6*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} c_1 e^{2 x}+\frac {1}{3} c_2 e^{3 x}+c_3 \]