Differential Equation Calculator

This differential equation solver helps to solve differential equations involving functions and their derivatives. Our tool supports first-order, second-order, and higher-order differential equations, providing step-by-step solutions. You can input problems manually, choose from a library of common equations, or upload an image of the equation for processing.

What is Differential Equations?

“Differential Equation is a mathematical equation that relates one or more functions to its derivatives.”

Explanation:

A differential equation describes the relationship between a quantity and its rate of change. Within this equation, function represents physical quantities while their derivatives show how those quantities change over time.

How To Solve Differential Equations?

Rearrange to isolate the terms of each variable on different sides
Perform integration on both sides, adding a constant of integration
Manipulate the equation to isolate the dependent variables
Substitute the given value to find the value of the constant of integration

Example:

Solve the differential equation: dy / dx = 3y

Solution:

Identify Type: This is a first-order linear differential equation.

Separate Variables: 1 / y dy = 3 dx

Integrate both sides: ∫1 / y dy = ∫ 3 dx

ln |y| =3x + C

Solve for y: y =e^{3x + C} = Ce^3x , Where C = e^C (simplified constant).

Apply Initial Condition: if y (0) = 2

2 = Ce⁰ ⟹ C = 2

Final Solution = y = 2e^3x

How to Use the Differential Equation Calculator?

Type the equation, paste it, or upload an image
Provide a short description if needed
Click on "Calculate" to get an instant solution

Our online Differential Equations Calculator provides you with a general solution of differential equations, allowing you to use it again and solve as many questions as you want.

FAQs:

Does the calculator provide step-by-step solutions?

Yes, this differential equation calculator provides you with stepwise solutions for solving equations.

What are the types of differential equations?

Ordinary differential equations (ODEs)
Partial differential equations (PDEs)
Linear differential equations
Nonlinear differential equations
Homogeneous differential equations
Non-homogeneous differential equations

Can I upload an image of an equation to solve it?

Our Differential Equation Calculator allows you to upload images for automatic recognition and solving.

What methods are used to solve differential equations?

Some common methods to solve differential equations include separation of variables, integration factors, characteristic equations, Laplace transform, and numeric methods.