10.7.20 problem 22

Internal problem ID [1268]
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 : 22
Date solved : Saturday, March 29, 2025 at 10:50:43 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-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: 0.070 (sec). Leaf size: 18

ode:=4*diff(diff(y(x),x),x)-y(x) = 0; 
ic:=y(0) = 2, D(y)(0) = beta; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2 \cosh \left (\frac {x}{2}\right )+2 \beta \sinh \left (\frac {x}{2}\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 25

ode=4*D[y[x],{x,2}]-y[x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==\[Beta]}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x/2} \left (-\beta +(\beta +1) e^x+1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + 4*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