72.12.19 problem 2 (a)

Internal problem ID [19592]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 04:40:25 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=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: 0.055 (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: 0.01 (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: 0.104 (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)
 

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