44.9.19 problem 2(a)

Internal problem ID [9241]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 2(a)
Date solved : Tuesday, September 30, 2025 at 06:15:33 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\mathrm e}^{2} \\ y^{\prime }\left (1\right )&=3 \,{\mathrm e}^{2} \\ \end{align*}

✓ Maple. Time used: 0.058 (sec). Leaf size: 10

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 0; 
ic:=[y(1) = exp(2), D(y)(1) = 3*exp(2)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-1+3 x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 12

ode=D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==0; 
ic={y[1]==Exp[2],Derivative[1][y][1]==3*Exp[2]}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{3 x-1} \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(1): exp(2), Subs(Derivative(y(x), x), x, 1): 3*exp(2)} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{3 x}}{e} \]