Solve a separable differential equation that integrates to inverse sine functions, and simplify the result using trigonometric identities.

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Solving a Separable Differential Equation with Inverse Trigonometric Functions

Parametric equations and vector functions core

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

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What you need first

Separable differential equations
Derivatives and integrals of inverse trigonometric functions
Trigonometric addition formulas
Simplifying compositions of trigonometric and inverse trigonometric functions

What this problem tests

Tests the ability to recognize and execute separation of variables, recall standard inverse trigonometric integrals, and apply trigonometric identities to simplify the final answer.

This problem is typical of a first course in differential equations or a Calculus II unit on separable equations, testing both integration skills and trigonometric simplification.

Solving a Separable Differential Equation with Inverse Trigonometric Functions

What you need first

What this problem tests

More on Parametric equations and vector functions