# What is the general solution of the differential equation? : #(d^4y)/(dx^4) - 4 y = 0#

There is an easy fix for each of these factors, such as:

The sum of the parts that make up the whole solution is:

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# y =Ae^(sqrt(2)x) + Be^(-sqrt(2)x) + Ccos(sqrt(2)x)+Dsin(sqrt(2)x) #

We have:

Complementary Role

The following is the auxiliary equation for [A]:

Thus, we have:

Parts of the solution are determined by the auxiliary equation's roots; if these parts are linearly independent, the solutions' superposition forms the complete general solution.

Thus, the homogeneous equation [A] has the following solution:

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The general solution of the differential equation (\frac{{d^4y}}{{dx^4}} - 4y = 0) is:

[y = C_1 e^{2x} + C_2 e^{-2x} + C_3 \cos(2x) + C_4 \sin(2x)]

Where (C_1), (C_2), (C_3), and (C_4) 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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