Vault Of Euclid

Solving a Separable Differential Equation with an Initial Condition

Parametric equations and vector functions warmup

Solve \(\frac{dy}{dx} = 3x^2y^2,\) given \(y(0) = \frac{1}{2}.\)

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What you need first

algebraic manipulation
power rule for integration
concept of a differential equation

What this problem tests

Tests the ability to separate variables, integrate using the power rule, and apply an initial condition to find the constant of integration.

This is a standard introductory problem in a calculus course covering basic differential equations.

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