64.10.3 problem 3

Internal problem ID [13338]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 3
Date solved : Monday, March 31, 2025 at 07:51:52 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \end{align*}

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

ode:=4*diff(diff(y(x),x),x)-12*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 24

ode=4*D[y[x],{x,2}]-12*D[y[x],x]+5*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: 0.156 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 12*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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