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Thursday, March 19, 2015

Eliminating Arbitrary Constant, 19

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


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










Substitute the values of A and B to the given equation and therefore, the final answer is