How do I compute the maximum value of

Aryan Salinas

Aryan Salinas

Answered question

2022-03-24

How do I compute the maximum value of the solution of this differential equation?
{dydt=f(y)=1+kϵkyeyy(0)=ϵ

Answer & Explanation

Kathleen Sanchez

Kathleen Sanchez

Beginner2022-03-25Added 7 answers

Step 1
Here is my approach to show that y=y
For the sake of contradiction assume that y<y. Because y(t) is a solution to your IVP we must have for any T>0 that
y(0)y(T)dx1+kϵkxex=0Tdt
This implies for any T>0
ϵy(T)dx1+kϵkxex=T
Take T+ and get
ϵydx1+kϵkxex=+
This is a contradiction since x11+kϵkxex is continuous on [ϵ,y]

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?