calculus calculators

First-Order ODE Solver

Solve first-order linear differential equations with constant coefficients

About this calculator

The First-Order ODE Solver is a powerful mathematical tool that solves first-order linear differential equations with constant coefficients. These equations appear frequently in physics, engineering, and applied mathematics to model exponential growth, decay processes, and dynamic systems. This calculator automatically finds the general or particular solution, saving time on complex algebraic manipulations and reducing calculation errors that commonly occur in manual solving.

How to use

Enter your first-order linear differential equation in standard form (dy/dx + py = q, where p and q are constants). Input any initial conditions if you need a particular solution. Click solve to get the complete solution with step-by-step workings showing the integration process.

Frequently asked questions

What format should I use for the differential equation?

Use standard form: dy/dx + py = q, where p and q are constants. For example: dy/dx + 2y = 5.

Can this solver handle initial value problems?

Yes, enter your initial condition (like y(0) = 3) to find the particular solution with the specific constant value.

What types of first-order equations can be solved?

This calculator solves linear first-order ODEs with constant coefficients, including homogeneous and non-homogeneous equations with exponential, polynomial, or constant forcing functions.