15.10.9 problem 9

Internal problem ID [3096]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:18:24 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y&=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)+16*diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 24

ode=D[y[x],{x,3}]-7*D[y[x],{x,2}]+16*D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.174 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) + 16*Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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