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?

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- Sep 25th 2009, 05:56 PMlataveesolution 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 AMchisigma
Let's write the DE as...

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Sep 26th 2009, 02:55 PMlataveeThanks!
Thank you so much, I understand!