Vault Of Euclid

Solving a Separable Differential Equation with Arctangent

Differential equations warmup

Solve the equation \[ y' = x(1 + y^2). \]

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What you need first

Separation of variables
Basic integration rules
The derivative of the arctangent function
Properties of inverse trigonometric functions

What this problem tests

Tests the ability to recognize a separable differential equation, perform basic integration, and solve for the dependent variable explicitly.

This is a standard introductory problem in a first course on ordinary differential equations or Calculus II.

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