71.1.16 problem 30

Internal problem ID [14254]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 30
Date solved : Monday, March 31, 2025 at 12:14:22 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x)+12*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{4 x}+c_3 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 30

ode=D[y[x],{x,3}]-7*D[y[x],{x,2}]+12*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} c_1 e^{3 x}+\frac {1}{4} c_2 e^{4 x}+c_3 \]

✓ Sympy. Time used: 0.159 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{3 x} + C_{3} e^{4 x} \]