First-Order Linear Differential Equation Solver: Step-by-Step Solutions

Integrating factor method for y′ + P(x)y = Q(x), with initial conditions. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

Solve $y^{\prime }+P(x)y=Q(x)$. Mode 1: $P$ constant and $Q$ built from polynomials, exponentials, sines and cosines. Mode 2: $P(x)=k/x$ and $Q$ a sum of powers of $x$ (solution for $x>0$).

How to use it

1. Enter your own numbers or functions in the boxes (an example is already filled in, or press Random example).
2. Check the equation preview, then press Solve step by step.
3. Reveal the solution one step at a time with Next step, or show everything at once.

Need the theory first? Read Section 2.3: Linear Equations and Bernoulli Equations, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 2 quiz.

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