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Homework Statement
Solve the integral equation for y(x):
y(x) = 1 + ∫ { [y(t)]^2 / (1 + t^2) } dt
(integral from 0 to x)
See attached image for the equation in a nicer format.
Homework Equations
Fundamental Theorem of Calculus
The Attempt at a Solution
dy/dx = y(x)^2 / (1 + x^2)
∫ dy/y^2 = ∫ dx/(1 + x^2)
1/y = arctan(x) + C
y = 1/arctan(x) + C
y(0) = 1 = 1/arctan(0) + C
C = 1 + 1/arctan(0)
Since arctan(0) = 0, the fraction is indeterminate.
In lectures we only did one practice example, so if anyone could give me a hand and point out where I am going wrong, it'll be greatly appreciated.
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