50.9.20 problem 2(b)

Internal problem ID [7956]
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(b)
Date solved : Sunday, March 30, 2025 at 12:39:08 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: 0.043 (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,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

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

\[ y(x)\to e^{2 x} \left (5 e^x-2\right ) \]

✓ Sympy. Time used: 0.164 (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)
 

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