__Category__: Differential Equations, Algebra"Published in Newark, California, USA"

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 c

_{1}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 c

_{1}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,