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Eliminate the arbitrary constant for
Solution:
Consider the given equation above and call this as equation #1, we have
Take the derivative with respect to x and call this as equation #2, we have
Since there are two arbitrary constants in the given equation, then we have to take the derivative of the given equation twice with respect to x. So, take the derivative of the above equation again with respect to x and call this as equation #3, we have
Using the equations #1 and #2:
Multiply equation #1 by 2 and multiply equation #2 by -1. Add the two equations in order to eliminate c1 and call this as equation #4, we have
Using the equations #1 and #3:
Multiply equation #1 by 4 and multiply equation #3 by -1. Add the two equations in order to eliminate c1 and call this as equation #5, we have
Equate equations #4 and #5, we have
Multiply both sides of the equation by 5, we have
Therefore,
