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Bernoulli ODE Solver

Solves y′ + P(x)y = Q(x)yⁿ by showing the substitution v = y^(1−n) that turns it into a linear equation, then integrating. The two degenerate cases are handled explicitly: n = 0 is already linear, n = 1 is separable.

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Bernoulli ODE Solver works straight from this page — free, instant, nothing to install. It covers n = 0 is already linear, n = 1 is separable — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Bernoulli ODE Solver do?

Solves y′ + P(x)y = Q(x)yⁿ by showing the substitution v = y^(1−n) that turns it into a linear equation, then integrating. The two degenerate cases are handled explicitly: n = 0 is already linear, n = 1 is separable.

What does it take into account?

It factors in n = 0 is already linear, n = 1 is separable. Change any of them and the output follows immediately.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Bernoulli ODE Solver different from First-Order ODE Solver?

They sit next to each other but answer different questions: First-Order ODE Solver is the one to open when you need it to solves dy/dx = f(x, y) from an initial condition with RK4, integrating outward in both directions, and plots the solution curve. Growth, decay, Newton cooling, logistic and separable cases are one click away. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Second-Order ODE Solver is the closest one after this: Solves a·y″ + b·y′ + c·y = g(x) with two initial conditions. Gives the characteristic roots, names the regime (undamped, under-damped, critically damped, over-damped), derives a particular solution for constant, polynomial and exponential forcing, and plots the result.

What else is worth having open alongside it?

Related rates solver and Absolute Value Equation Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

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