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Eliminating Arbitrary Constant, 14

__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 with respect to x twice. Again, take the derivative on both sides of the equation with respect to x, we have
Substitute the value of c_{2} to the first derivative equation and therefore, the final answer is