50.9.21 problem 2(c)

Internal problem ID [7957]
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(c)
Date solved : Wednesday, March 05, 2025 at 05:20:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 11

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = 0; 
ic:=y(0) = 0, D(y)(0) = 5; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{3 x} x \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 13

ode=D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 5 e^{3 x} x \]

✓ Sympy. Time used: 0.168 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 x e^{3 x} \]