Find an interval centered about x=0 for which the given IVP has a unique solution:
y" + (tan x)y=e^x y(0)=1, y'(0)=0
How would I find the interval?
Let's write the DE as...
, , (1)
Now we remember that necessary condition to have one and only one solution in an interval of the x variable is that the coefficient of the term doesn't vanish in that inteval, so that it exists one and only one solution of (1) for ...