Analytic Methods for Solving First-Order ODE

The general form of a first-order differential equation is

Here t is the independent variable and y is the dependent variable. The goal is to find the unknown function y(t).

Classes of First-Order ODE

It is said that a differential equation is solved exactly if the answer can be expressed in the form of an integral. The following classes of first-order ode can be solved exactly:

• directly integrable

  

  (derivative function depends on independent variable only)

• linear

  

• separable

  

• homogeneous

  

• exact

  

  where the partial derivatives satisfy f_y=g_t.

• Bernoulli

  

  where n doesn't equal 1.

This list is not exhaustive, but covers core classes of first-order ode that can be solved exactly.

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