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Monday, March 23, 2015

Eliminating Arbitrary Constant, 23

Category: Differential Equations

"Published in Newark, California, USA"

Eliminate the arbitrary constant for


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    

Add the first and second derivative equations, we have


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