62.22.4 problem Ex 4

Internal problem ID [12855]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
Problem number : Ex 4
Date solved : Monday, March 31, 2025 at 07:22:51 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+9*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 x +c_2 \right ) {\mathrm e}^{3 x}+c_1 \]

✓ Mathematica. Time used: 3.491 (sec). Leaf size: 89

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+9*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \int _1^xe^{3 K[1]} (c_1+c_2 K[1])dK[1]+c_3 \\ y(x)\to \frac {1}{3} c_1 e^{3 x}-\frac {e^3 c_1}{3}+c_3 \\ y(x)\to \frac {1}{9} c_2 e^{3 x} (3 x-1)-\frac {2 e^3 c_2}{9}+c_3 \\ \end{align*}

✓ Sympy. Time used: 0.163 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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