88.14.8 problem 8

Internal problem ID [24096]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 93
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:59:12 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\frac {327 y^{\prime }}{100}-\frac {21 y}{50}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+327/100*diff(y(x),x)-21/50*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{\frac {x \sqrt {123729}}{100}}+c_2 \right ) {\mathrm e}^{-\frac {\left (327+\sqrt {123729}\right ) x}{200}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 38

ode=D[y[x],{x,2}]+327/100*D[y[x],x]-42/100*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\frac {1}{200} \left (327+\sqrt {123729}\right ) x} \left (c_2 e^{\frac {\sqrt {123729} x}{100}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-21*y(x)/50 + 327*Derivative(y(x), x)/100 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (-327 + \sqrt {123729}\right )}{200}} + C_{2} e^{- \frac {x \left (327 + \sqrt {123729}\right )}{200}} \]