Eliminating Arbitrary Constant, 17

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 again with respect to x for the above equation as follows   

Multiply the first derivative equation by -2 and then add it to the second derivative equation, we have

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Multiply the first derivative equation by -2 and then add it to the second derivative equation, we have

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Substitute the values of c₁ and c₂ to the given equation and therefore, the final answer is

Eliminating Arbitrary Constant, 16

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 again with respect to x for the above equation as follows  

If you add the first and second derivative equations, then we can solve for the value of c₁ as follows 

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If you subtract the first and second derivative equations, then we can solve for the value of c₂ as follows

-()

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Substitute the values of c₁ and c₂ to the given equation and therefore, the final answer is