85.37.3 problem 1 (c)

Internal problem ID [22746]
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 175
Problem number : 1 (c)
Date solved : Thursday, October 02, 2025 at 09:14:17 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to e^{-2 x} \left (c_1 e^{4 x}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 15

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

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