Integrating y’ = 1/(2e√x) to Find a Solution for the Given Derivative Problem

y’=1/(2e√x)

The given expression is a derivative problem

The given expression is a derivative problem. To find the solution, we need to integrate the given expression with respect to x.

Integrating y’ = 1/(2e√x) with respect to x, we get:

∫y’ dx = ∫1/(2e√x) dx

Integration of 1/(2e√x) can be done using substitution. Let’s substitute u = √x, then du = (1/2√x)dx. Rearranging this, we have 2√x dx = du.

Now, our integral becomes:

∫1/(2e√x) dx = ∫1/2e du

Integrating ∫1/2e du gives us:

(1/2) * ∫1/e du

The integral of 1/e is simply e^(-u) plus a constant of integration.

Therefore, the solution is:

y = (1/2) * e^(-√x) + C

where C is the constant of integration.

This is the general solution to the given differential equation. To find a particular solution, we need additional information such as initial conditions.

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