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First-Order Differential Equation

Calculate First-Order Differential Equation instantly with the exact formula and a worked example.

First-Order Differential Equation

dy/dx = ky, k
y(0)
x
y(x) = y₀·e^(kx)
2.7183
Calculate First-Order Differential Equation instantly with the exact formula and a worked example.

More about: First-Order Differential Equation

What it calculates

The “First-Order Differential Equation” calculator computes y(x) = y₀·e^(kx) from 3 parameters: dy/dx = ky, k, y(0), x.

A core calculation for studying, engineering tasks, and checking solutions.

Example calculation

With parameters dy/dx = ky, k = 0.5, y(0) = 1, x = 2 the result is 2.72.

How to use

  1. Enter dy/dx = ky, k, y(0) and x — each field above is adjustable with a slider.
  2. y(x) = y₀·e^(kx) is calculated automatically as you type.
  3. Check the worked example below to see the formula applied to real numbers.
  4. Copy the result or bookmark this calculator.

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FAQ

How is First-Order Differential Equation calculated?
The First-Order Differential Equation calculator computes y(x) = y₀·e^(kx) from dy/dx = ky, k, y(0), x. Enter your values above and the exact formula is applied instantly; a worked example with real numbers is shown below.
Is the First-Order Differential Equation calculator free?
Yes. It is completely free, needs no signup, runs entirely in your browser, and sends no data to any server.

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