Periodic Solution to Differential Equation

[rosogollah]

For each epsilon greater than 0, show that the differential equation x'=x^2-1-cos(t)-epsilon has at least one periodic solution with 0 less than x(t) less than or equal to (2+epsilon)^1/2

 

[jambaugh]

It's obvious. There I've proved it!

Seriously review the homework submission guidelines for this forum. As with my answer, your question needs to show a bit more to be helpful.