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Friday, March 6, 2015

Eliminating Arbitrary Constant, 6

Category: Differential Equations

"Published in Newark, California, USA"

Eliminate the arbitrary constant for


ω is a parameter; not to be eliminated.

Solution:

Consider the given equation above 


Take the derivative on both sides of the equation with respect to t, we have 






Take the derivative on both sides of the equation again with respect to t, we have  







Substitute the above equation to the given equation and therefore, the final answer is





Thursday, March 5, 2015

Eliminating Arbitrary Constant, 5

Category: Differential Equations

"Published in Newark, California, USA"

Eliminate the arbitrary constant for



Solution:

Consider the given equation above  


Divide both sides of the equation by x², we have 





Take the derivative on both sides of the equation with respect to x, we have 








Multiply both sides of the equation by x³dx and therefore, the final answer is





Wednesday, March 4, 2015

Eliminating Arbitrary Constant, 4

Category: Differential Equations

"Published in Newark, California, USA"

Eliminate the arbitrary constant for


Solution:

Consider the given equation above 


Divide both sides of the equation by y, we have




Take the derivative on both sides of the equation with respect to x, we have






Multiply both sides of the equation by y²dx and therefore, the final answer is