Separation of variables.Please demonstrate how you accomplished the task. Then we can talk.
Looks good to me.Separation of variables.
dy/dx = e^-y
e^ydy = dx
integrate both sides u get
e^y = x + c
y = log (x+c)
y(0)=0 so
0 = log (0 + c)
c = 1
y(0.5) = log (1.5) = 0.4054651081
This is how I did it.
hahaha it's for my assignment, he asked us to find 3 methods to solve it thank you for your help anyway!This is NOT a "linear equation" so some of the methods I mention in your previous thread will not work. Yes, it is very easy to solve \(\displaystyle \frac{dy}{dx}= e^{-y}\) by integration by parts. I still don't know why you need two other methods!
I have some difficulty in continuing the equation.Looks good to me.
Now let u = e^-y
u = e^(-y)I have some difficulty in continuing the equation.
y' = e^-y, let u = e^-y so du/dx = -e^-y.................................. Incorrect
is it right or do I need to make it in terms of y? I am sorry I'm new to this.
i have gotten the answer, thank you so much for your help! ?u = e^(-y)
u' = - e^(-y) * dy/dx = - u2