81.4.3 problem 3

Internal problem ID [18657]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 48
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 12:08:56 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 25

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

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