Solve Differential Equation Calculator
A calculator to solve first-order ordinary differential equations (ODEs) of the form dy/dx = f(x,y). Enter the function f(x,y) and initial conditions to obtain an approximate numerical solution using the Euler method.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to use the Solve Differential Equation Calculator
- Enter the function f(x,y): Type the right-hand side of the differential equation dy/dx = f(x,y). Use standard math notation (e.g.,
x + y,Math.sin(x),x*y). - Set initial conditions: Provide the starting point (x₀, y₀). For example, x₀ = 0, y₀ = 1.
- Define the target: Enter the x value where you want the approximate solution (x target). It must be greater than x₀.
- Choose step size h: A smaller h gives more accurate results but more steps. Must be positive (e.g., 0.1).
- Click "Solve": The calculator uses Euler's method to approximate y at the target x. The result appears in green, and each step is listed below.
Note: All inputs are numeric (no units). The function must be valid JavaScript math. If an error occurs, a red message will explain the issue.
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Frequently Asked Questions
This calculator solves first-order ordinary differential equations of the form dy/dx = f(x,y) using Euler's method. It provides a numerical approximation, not an exact symbolic solution.
Use standard mathematical notation with x and y as variables. For example, for dy/dx = x + y, enter 'x + y'. You can use functions like Math.sin(x), Math.exp(y), etc.
Euler's method is a simple numerical technique for approximating solutions to ODEs. It uses the derivative at the current point to step forward by a small step size h, updating y as y_new = y + h * f(x,y).
