10.9.3 problem 3

Internal problem ID [1305]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 12:28:39 PM
CAS classification : [[_2nd_order, _missing_x]]

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

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

ode:=4*diff(diff(y(x),x),x)-4*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {x}{2}}+c_2 \,{\mathrm e}^{\frac {3 x}{2}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {x}{2}} + C_{2} e^{\frac {3 x}{2}} \]