78.12.19 problem 2 (a)

Internal problem ID [18227]
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, March 13, 2025 at 11:49:41 AM
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: 0.025 (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,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (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]
 

\[ y(x)\to e^{3 x-1} \]

✓ Sympy. Time used: 0.163 (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)
 

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