75.4.3 problem 3

Internal problem ID [19942]
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 : Thursday, October 02, 2025 at 05:04:22 PM
CAS classification : [[_3rd_order, _missing_x]]

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

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

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

\[ y = c_1 +c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to c_1 e^x+\frac {1}{2} c_2 e^{2 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{x} + C_{3} e^{2 x} \]