23.3.1 problem 7(a)

Internal problem ID [4142]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 7(a)
Date solved : Monday, January 27, 2025 at 08:39:59 AM
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: 0.004 (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)
 

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

✓ Solution by Mathematica

Time used: 0.029 (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]
 

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