15.9.22 problem 36

Internal problem ID [3079]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 36
Date solved : Tuesday, March 04, 2025 at 03:58:21 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} +c_2 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 25

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.135 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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