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 : Sunday, March 30, 2025 at 02:40:55 AM
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: 0.029 (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]
 

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

✓ Sympy. Time used: 0.137 (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)
 

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