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Saturday, March 21, 2015

Eliminating Arbitrary Constant, 21

Category: Differential Equations

"Published in Vacaville, California, USA"

Eliminate the arbitrary constant for


where a and b are parameters.

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 -2a and then add it to the second derivative equation, we have 


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but 
     
Therefore, the final answer is