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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