7.10.21 problem 21

Internal problem ID [291]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 21
Date solved : Tuesday, March 04, 2025 at 11:07:17 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=7\\ y^{\prime }\left (0\right )&=11 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+3*y(x) = 0; 
ic:=y(0) = 7, D(y)(0) = 11; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{3 x}+5 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==0; 
ic={y[0]==7,Derivative[1][y][0] ==11}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.156 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 7, Subs(Derivative(y(x), x), x, 0): 11} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (2 e^{2 x} + 5\right ) e^{x} \]