10.7.21 problem 23

Internal problem ID [1269]
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 : 23
Date solved : Saturday, March 29, 2025 at 10:50:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-(2*alpha-1)*diff(y(x),x)+alpha*(alpha-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\alpha x} \left (c_1 +c_2 \,{\mathrm e}^{-x}\right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-(2*\[Alpha]-1)*D[y[x],x]+\[Alpha]*(\[Alpha]-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{(\alpha -1) x}+c_2 e^{\alpha x} \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
Alpha = symbols("Alpha") 
y = Function("y") 
ode = Eq(Alpha*(Alpha - 1)*y(x) - (2*Alpha - 1)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{- x}\right ) e^{\mathrm {A} x} \]