15.9.9 problem 23

Internal problem ID [3066]
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 : 23
Date solved : Sunday, March 30, 2025 at 01:17:52 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \left (c_1 \,{\mathrm e}^{x \sqrt {5}}+c_2 \right ) {\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) x}{2}} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 35

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

\[ y(x)\to e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) x} \left (c_2 e^{\sqrt {5} x}+c_1\right ) \]

✓ Sympy. Time used: 0.175 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (3 - \sqrt {5}\right )}{2}} + C_{2} e^{\frac {x \left (\sqrt {5} + 3\right )}{2}} \]