# What is the general solution of the differential equation # y''' + 4y'' = 0 #?

# y = Ax+B + Ce^(-4x) #

We have:

Complimentary Function

The Auxiliary equation associated with the homogeneous equation of [A] is:

The roots of the axillary equation determine parts of the solution, which if linearly independent then the superposition of the solutions form the full general solution.

Thus the solution of the homogeneous equation is:

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The general solution of the differential equation ( y''' + 4y'' = 0 ) is ( y(x) = c_1 + c_2e^{-4x} + c_3xe^{-4x} ), where ( c_1, c_2, ) and ( c_3 ) 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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