Free counters!

Wednesday, March 18, 2015

Eliminating Arbitrary Constant, 18

Category: Differential Equations

"Published in Vacaville, California, USA"

Eliminate the arbitrary constant for


Solution:
   

Consider the given equation above 


Take the derivative on both sides of the equation with respect to x, we have 






Since there are two constants in the given equation, then we need to take the derivative again with respect to x for the above equation as follows  







Multiply the first derivative equation by -1 and then add it to the second derivative equation, we have 


--------------------------------------------


Substitute the value of c2 to the first derivative equation, we have
 
 
 
 
 
 

Substitute the values of c1 and c2 to the given equation and therefore, the final answer is