# Differential Equation Calculator

Differential Equation Calculator calculates the function for the given first-order differential equation and the value of the function. An equation that contains the derivative of a function is called a differential function.

## What is Differential Equation Calculator?

Differential Equation Calculator is an online tool that helps to calculate the function for the given first-order differential equation and the value of the function. This online differential equation calculator helps you to calculate the function in a few seconds. To use this differential equation calculator, enter the derivative function and the value of the function in the given input box.

## How to Use Differential Equation Calculator?

Please follow the steps below to find the function using an online differential equation calculator:

**Step 1:**Go to Cuemath’s online differential equation calculator.**Step 2:**Enter the differential function(y') and the value of the function y(0) in the given input box of the differential equation calculator.**Step 3:**Click on the**"Solve"**button to calculate the function for the given first-order differential equation and the value of the function.**Step 4:**Click on the**"Reset"**button to clear the fields and enter the new function and values.

## How Differential Equation Calculator works?

A **differential equation** is defined as an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables).

The general form of first-order differential equation is given by y' + p(x)y = Q(x) where P and Q are functions of x alone.

Let us understand this with the help of the following example.

**Solved Example on Differential Equation**

Find the function for the first-order differential equation y' = x^{2 }and y(0) = 2 and verify it using the differential equation calculator?

**Solution**:

Given: y' = x^{2} and y(0) = 2

Integrate the given first order differential equation y(x) = x^{3} / 3 + c

y(0) = 2 ⇒ (0)^{3} / 3 + c = 2

⇒ c = 2

y(x) = x^{3} / 3 + 2

Now, try the differential equation calculator and find the value of function for:

- y' = 3x
^{2}and y(0) = 5 - y' = x
^{3}and y(0) = 7