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Tuesday, March 17, 2015

Eliminating Arbitrary Constant, 17

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


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