# What is the general solution of the differential equation # y'' - 10y' +25 = 0#?

# y = Axe^(5x) + Be^(5x) #

We have:

Complimentary Function

The associated Auxiliary equation is:

Thus the solution of the homogeneous equation is:

Confirming the quoted solution

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The general solution of the differential equation ( y'' - 10y' + 25 = 0 ) is:

[ y(t) = c_1 e^{5t} + c_2 t e^{5t} ]

Where ( c_1 ) and ( c_2 ) are arbitrary constants.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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