- #1
KillerZ
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- 0
Homework Statement
Find an interval centered about x = 0 for which the given initial-value problem has a unique solution.
[tex]y^{''} + (tanx)y = e^{x}[/tex]
[tex]y(0) = 1[/tex] [tex]y^{'}(0) = 0[/tex]
Homework Equations
[tex]a_{i}(x), i=0,1,2,3,...,n[/tex] is continuous and
[tex]a_{n} \neq 0[/tex] for every x in I.
The Attempt at a Solution
[tex]a_{0} = tanx[/tex] is zero at x = 0
I am not sure if this is correct because tanx is continuous everywhere except at pi/2, 3pi/2, etc... so would interval be:
[tex]I = (0,\infty) or (-\infty , 0)[/tex]
or
[tex]I = (0,\pi/2) or (-\pi/2 , 0)[/tex]