71.10.1 problem 1

Internal problem ID [14425]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 1
Date solved : Monday, March 31, 2025 at 12:26:55 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);
 

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

✓ Mathematica. Time used: 0.014 (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]
 

\[ y(x)\to e^{-3 x/2} \left (c_2 e^{2 x}+c_1\right ) \]

✓ Sympy. Time used: 0.157 (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)
 

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