10.7.22 problem 24

Internal problem ID [1270]
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 : 24
Date solved : Saturday, March 29, 2025 at 10:50:47 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+(3-alpha)*diff(y(x),x)-2*(alpha-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{x \left (\alpha +1\right )}+c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

ode=D[y[x],{x,2}]+(3-\[Alpha])*D[y[x],x]-2*(\[Alpha]-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_1 e^{\alpha x+x}+c_2\right ) \]

✓ Sympy. Time used: 0.184 (sec). Leaf size: 17

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

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