50.9.14 problem 1(n)

Internal problem ID [7950]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 1(n)
Date solved : Sunday, March 30, 2025 at 12:39:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=4*diff(diff(y(x),x),x)-8*diff(y(x),x)+7*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 38

ode=4*D[y[x],{x,2}]-8*D[y[x],x]+7*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]

✓ Sympy. Time used: 0.149 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(7*y(x) - 8*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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