Solve a first-order separable differential equation by integrating to get inverse tangents and simplifying with the tangent addition formula.

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Solving a Separable Differential Equation with Inverse Tangents

Parametric equations and vector functions core

Solve \(\frac{dy}{dx} = \frac{1+y^2}{1+x^2}.\)

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What you need first

Separable differential equations
The integral of 1/(1+x^2)
The tangent addition formula
Inverse trigonometric functions

What this problem tests

Tests the ability to recognize a separable differential equation, integrate rational functions to inverse trigonometric functions, and simplify the result algebraically.

This problem is typical of introductory differential equations or Calculus II courses, testing both separation of variables and trigonometric identities.

Solving a Separable Differential Equation with Inverse Tangents

What you need first

What this problem tests

More on Parametric equations and vector functions