# solution interval for IVP

• Sep 25th 2009, 05:56 PM
latavee
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?
• Sep 26th 2009, 10:49 AM
chisigma
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

$\chi$ $\sigma$
• Sep 26th 2009, 02:55 PM
latavee
Thanks!
Thank you so much, I understand!