Math Help - solution interval for IVP

1. solution interval for IVP

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?

2. Let's write the DE as...

$\cot x\cdot y^{''} + y = e^{x}\cdot \cot x$ , $y(0)=1$ , $y^{'} (0)= 0$ (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 $y^{''}$ doesn't vanish in that inteval, so that it exists one and only one solution of (1) for $-\frac{\pi}{2}...

Kind regards

$\chi$ $\sigma$

3. Thanks!

Thank you so much, I understand!