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Wednesday, March 25, 2015

Eliminating Arbitrary Constant, 25

Category: Differential Equations

"Published in Newark, 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    





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





Multiply the first derivative equation by -2 and add it to the second derivative equation, we have


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Substitute the value of c1 to the second derivative equation, we have 












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