10.7.24 problem 26

Internal problem ID [1272]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 26
Date solved : Saturday, March 29, 2025 at 10:50:50 PM
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 (0\right )&=2\\ y^{\prime }\left (0\right )&=\beta \end{align*}

✓ Maple. Time used: 0.064 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)+6*y(x) = 0; 
ic:=y(0) = 2, D(y)(0) = beta; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} \left (\left (\beta +6\right ) {\mathrm e}^{x}-4-\beta \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 23

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

\[ y(x)\to e^{-3 x} \left (-\beta +(\beta +6) e^x-4\right ) \]

✗ Sympy

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(0): 2, Subs(Derivative(y(x), x), x, 0): beta} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : property object is not iterable