๐Differential Equation Solver
Solve separable, linear, and homogeneous first-order ODEs with steps and a slope field.
Free Differential Equation Solver
Working through a first-order differential equation and want to check your method as well as your answer? Our free differential equation solver handles separable, linear, and homogeneous equations. Enter your equation in dy/dx = f(x,y) form, and the solver detects which method applies โ then shows every step, from separating variables or computing an integrating factor through to the final solution.
Add an initial condition and it solves for the constant to give you the particular solution, not just the general family. A slope field graph shows the direction field across the plane with a representative solution curve drawn directly on top. If an equation doesn't match a supported closed-form method, it says so clearly instead of guessing.
Enter your equation to get started. No sign-up, no downloads, no limits.
About the Differential Equation Solver
Features
Type detection
Classifies the equation as separable, linear, or homogeneous.
Step-by-step solving
Separation of variables or integrating-factor steps for supported templates.
General and particular solution
Solves for the constant when an initial condition is given.
Slope-field visualization
A direction field with a solution curve drawn on top.
Frequently Asked Questions
How does the differential equation solver work?
Enter your equation in dy/dx = f(x,y) form, and it detects the type (separable, linear, or homogeneous) and solves it step by step when a matching closed-form method is available.
Is it free?
Completely free, no sign-up, downloads, or limits.
What types of equations are supported?
First-order separable, linear (via integrating factor), and homogeneous equations that match a supported closed-form template.
Can it solve with an initial condition?
Yes, add x0 and y0 and it solves for the constant to give the particular solution.
What if my equation isn't one of the supported types?
It tells you clearly rather than producing an incorrect result, and still shows the slope field.
What is a slope field?
A grid of short line segments showing the equation's direction at each point; the solver draws it with a solution curve on top.
Does it show the general solution too?
Yes, the general solution with constant C is shown alongside the particular solution when an initial condition is given.
What is an integrating factor?
A function used to solve linear first-order equations; the solver applies it as part of the closed-form templates it supports.
Is my input stored anywhere?
No; everything runs in your browser and isn't stored or sent anywhere.
Does it work on mobile?
Yes, fully responsive, including the slope-field graph and step-by-step panel.