64.10.13 problem 13

Internal problem ID [13348]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 13
Date solved : Monday, March 31, 2025 at 07:52:07 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=0 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)+7*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=D[y[x],{x,3}]-5*D[y[x],{x,2}]+7*D[y[x],x]-3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.183 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) + 7*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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