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Consider the differential equation 4y" - 4y'y = 0; ex/2, xex/2. What is the solution to this equation?

User DanubePM
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1 Answer

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Final answer:

To solve the given differential equation, we separate variables and integrate both sides of the equation.

Step-by-step explanation:

To solve the differential equation 4y" - 4y'y = 0, we can first separate the variables. Then, we can integrate each side to find the general solution.

Let's start by separating the variables. We can write the differential equation as:

4y" - 4y'y = 0

4y" = 4y'y

Next, we divide both sides by 4y'y:

y"/y' = 1/y

Now, we can integrate both sides with respect to x:

∫(y"/y')dx = ∫(1/y)dx

Using the properties of logarithms, we have:

ln|y'| = ln|y| + C1

where C1 is the constant of integration.

Finally, we can solve for y' by exponentiating both sides:

y' = y * e^C1

This is a separable differential equation that can be solved by separating the variables and integrating.

User Cldwalker
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