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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.