Variation of Parameters Calculator: Step-by-Step Solutions

Wronskian, u₁′ and u₂′, integration and the particular solution. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

Choose a case. Trig: $y^{\prime \prime }+k^{2}y=Ag(kx)$. Repeated root: $y^{\prime \prime }-2r{y}^{\prime }+r^{2}y=A{e}^{rx}g(x)$. General: any second-order constant-coefficient equation with a right side built from polynomials, exponentials, sines and cosines.

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 4.4: Variation of Parameters, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 4 quiz.

All computations run in your browser; nothing is sent to a server.