determine the values of r for which  erx  satisfies the differential equation, we substitute  f(x) = erx  in the equation, 6f ''(x) + 3f '(x) − 3f(x) = 0. Thus, we need to find f '(x) and f ''(x). f(x)  =  erx   f '(x)  =          f ''(x)  =

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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o determine the values of r for which 

erx

 satisfies the differential equation, we substitute 

f(x) = erx

 in the equation,

6f ''(x) + 3f '(x) − 3f(x) = 0.


Thus, we need to find f '(x) and f ''(x).

f(x)  =  erx
 
f '(x)  = 
 
 
 
 
f ''(x)  = 
 
 
 
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