- #1
asmani
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Homework Statement
Find [itex]y(\pi/3)[/itex] in the following integral equation:
$$y(x)=e^{-\int_{1}^{x}\frac{y(t)}{\sin^2(t)}dt}$$
Homework Equations
The Attempt at a Solution
Differentiating both sides gives a differential equation with the general solution [itex]y(x)=(-\cot(x)+c)^{-1}[/itex], and since y(1)=1, we have [itex]c=1+\cot(1)[/itex].
Here is two questions:
1. The hint says the answer is [itex]y(\pi/3)=3/(6-\sqrt{3})[/itex]. Is this correct?
2. Is there any shortcut way to solve this problem without differentiating?
Thanks in advance.