86.5.17 problem 17

Internal problem ID [23131]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5a at page 74
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:23:13 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

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

\[ y = \left (c_1 \,{\mathrm e}^{\sqrt {7}\, x}+c_2 \right ) {\mathrm e}^{-\frac {\sqrt {7}\, x}{2}} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to e^{-\frac {\sqrt {7} x}{2}} \left (c_1 e^{\sqrt {7} x}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {\sqrt {7} x}{2}} + C_{2} e^{\frac {\sqrt {7} x}{2}} \]