Integrating Factor Calculator

About this calculator

For a first-order linear ODE of the form dy/dx + Py = Q, multiplying both sides by the integrating factor μ = e^(∫P dx) turns the left-hand side into the exact derivative d/dx(μy), which can then be integrated directly to solve for y. When P is constant, the integral simplifies to μ = e^(Px), evaluated at whatever x value you enter.

This method — sometimes credited to Leibniz — is the standard technique taught in introductory differential-equations courses for solving linear (but not necessarily separable) first-order equations, and it underlies models in circuit analysis (RC/RL charging curves), population growth with a constant harvesting rate, and Newton's law of cooling. Students and engineers use this calculator to check the integrating factor for a given constant coefficient before carrying out the rest of the solution by hand.