Question

dy/dx+y=1/e*x. find general solution

Answer 1

hiii friend!!!
================================================================
Answer:y=Aex+ex
================================================================
Explanation:

We have:

dydx=y(1+ex)

This is a first Order Separable Differential Equation, we can collect terms by rearranging the equation as follows

1ydydx=(1+ex)

And now we can "separate the variables" to get

∫ 1y dy=∫ 1+ex dx

And integrating gives us:

ln|y|=x+ex+C∴|y|=ex+ex+C∴|y|=ex+exeC

And as ex>0∀x∈R, we can write the solution as:

∴y=Aex+ex
================================================================
i think it may help u !!!!!