85.42.4 problem 1 (d)

Internal problem ID [22773]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 180
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 09:14:32 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: 0.012 (sec). Leaf size: 38

ode=4*D[y[x],{x,2}]-8*D[y[x],{x,1}]+7*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} 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 ) \end{align*}

✓ Sympy. Time used: 0.109 (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)
 

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