Microsoft Excel is a powerful tool that can perform different mathematical operations. In this article, we will learn to solve a differential equation in Excel. A differential equation defines the relationship between one or more functions and their derivatives. Today, we will show step-by-step procedures to solve a differential equation in Excel. Using these steps, you can easily solve any differential equation in Excel. So, without any delay, letâ€™s start the discussion.

**Table of Contents**Expand

## What Is a Differential Equation?

A differential equation is an equation that contains one or more functions and the derivatives of one variable with respect to another variable. The differential equation can be written as:

`dy/dx=f(x)`

We have different order differential equations. The highest order of the derivative is called the order of the differential equation. Differential equations are mainly used to calculate growth and decay over time. Also, these equations are used to create different models. We can also see a huge application of differential equations in the field of physics.

## How to Solve Differential Equation in Excel: With Easy Steps

Today, we will demonstrate the procedures to solve a first-order differential equation using Eulerâ€™s method in Excel. Letâ€™s take a look at the question we will be solving today.

Suppose, we have a differential equation **dy/dt+y=t** and an initial value **y(0)=0.5**. So, the equation can be written as **dy/dt = t-y**. We need to compute the **y**â€“**values **in a **time interval (0,1.2)**. Letâ€™s follow the steps below to see how we can solve the differential equation.

### STEP 1: Create Dataset

- Firstly, we need to create a dataset to insert the
**iteration number**(**n**),**time value**(**t**),**y value**,**y**â€“**exact****value**, and**delta_t**. - The
**delta_t**is the separation value. - Also, you can display the equations to find the
**t(n+1)**and**y(n+1)**values. We will implement these equations in the following sections. - We have also added the
**time interval**and**initial value**to make the calculation easy.

### STEP 2: Apply Formula for Time Values & Y-values

- Secondly, we will apply formulas to calculate the
**time values**and**y-values**. - At the start of the iteration,
**n**is**0**,**t**is**0**, and**y**is**5**. - Now, insert these values in
**Cells B5**,**C5**, and**D5Â**respectively.

- After that, we will insert a formula to calculate the
**t-values**. - To do so, select
**Cell C6**and type the formula below:

`=C5+$G$5`

- Press
**Enter**.

- In the following step, we will find the
**y-values**. - So, select
**Cell D6**and type the formula below:

`=D5+(C5-D5)*$G$5`

- Press
**Enter**to see the result.

### STEP 3: Fill Columns

- In the third step, we will fill the values with the
**n**,**t**, and**yÂ**columns. - Firstly, we will fill the iteration number (
**n**) column. - To find the number of iterations, we need to divide the
**time interval**by the**delta_t value**. - In our case, iteration number (
**n**) = (**2**/**0.1**) =**12**. - So, we need to fill the iteration column from
**0**to**12**.

- After that, select both
**Cells C6**&**D6**and drag the**Fill HandleÂ**down.

- Finally, you will get all the
**t**and**y**â€“**values**.

### STEP 4: Plot Data

- At this moment, we need to plot the
**t**and**y**â€“**values**. - For that purpose, select the
**range C4:D17**.

- After that, go to the
**Insert**tab and click on the**Insert Scatter**icon. A drop-down menu will appear. - Select
**Scatter with Lines**from there.

- As a result, you will see a chart on the sheet.
- You can change the chart title according to your preferences.

### STEP 5: Format Axis

- In
**step 5**, we will format the axis of the graph. - To do so,
**double**â€“**click**on the**horizontal axis**. It will open the**Format Axis**options on the right side of the sheet. - Set the
**Minimum**value to**0**and**Maximum**value to**1.2**in the**Bounds**section, and press**Enter**to proceed.

- Similarly,
**double**â€“**click**on the**vertical axis**. - Then, set the
**Minimum**value to**0.****3**and**Maximum**value to**0.65**in the**Bounds**section, and press**Enter**to proceed.

- As a result, the graph will look like the picture below.

**Read More:** How to Solve an Equation for X When Y is Given in ExcelÂ

### STEP 6: Find the Exact Solution

- Now, we will calculate the exact solution of the differential equation and match it with the numerical values.
- In our case, the exact solution of the differential equation is
**y = -1 + t + 1.5*exp(-t)**. - So, select
**Cell E5**and type the formula below:

`=-1+C5+1.5*EXP(-C5)`

- After that, press
**Enter**and drag the**Fill HandleÂ**down.

- Finally, you will know the
**y-values**of the exact solution.

### STEP 7: Plot the Exact Solution on the Same Chart

- To compare the
**y-values**of the exact solution with the numerical values, we need to plot them on the same chart. - To do so,
**right**â€“**click**on the chart to open the menu. - Click on the
**Select DataÂ**option.

- In the
**Select Data Source**dialog box, click on**Add**.

- Now, insert the
**Series X**and**Y**values in the**Edit SeriesÂ**box.

- Finally, click
**OK**to get the plot of the exact solution.

**Read More:** How to Solve 2 Equations with 2 Unknowns in Excel

### Final Output

- Finally, if we change the
**delta_t**value in**Cell G5**, then the whole dataset will automatically update and show the solution for the updated**delta_tÂ**value.

- Furthermore, the graphs will also update automatically.

**Read More:** How to Solve Polynomial Equation in Excel

**Download Practice Book**

You can download the practice book from here.

## Conclusion

In this article, we have discussed step-by-step procedures to solve a differential equation in Excel. I hope this article will help you to perform your tasks efficiently. Furthermore, we have also added the practice book at the beginning of the article. To test your skills, you can download it to exercise.Â Lastly, if you have any suggestions or queries, feel free to ask in the comment section below.

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