Solve the basic first-order separable differential equation dy/dx = ky.

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Solving the Exponential Growth Differential Equation

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Solve \( \frac{dy}{dx} = ky \).

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What you need first

basic integration
properties of logarithms and exponentials
the concept of a differential equation

What this problem tests

Tests the ability to recognize and solve a basic separable differential equation, including the algebraic manipulation of the constant of integration.

This is the foundational differential equation for modeling exponential growth and decay, such as population growth or radioactive decay, typically introduced early in a calculus course.

Solving the Exponential Growth Differential Equation

What you need first

What this problem tests

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