72.12.20 problem 2 (b)

Internal problem ID [19593]
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 (b)
Date solved : Thursday, October 02, 2025 at 04:40:25 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=11 \\ \end{align*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+5*y(x) = 0; 
ic:=[y(0) = 3, D(y)(0) = 11]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{x}+2 \,{\mathrm e}^{5 x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 16

ode=D[y[x],{x,2}] -6*D[y[x],x]+5*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] == 11}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x+2 e^{5 x} \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 11} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (2 e^{4 x} + 1\right ) e^{x} \]