2Solving First-Order Equations

DOI: 10.1201/9781003214526-2

  • Separable equations

  • First-order linear equations

  • Exact equations

  • Orthogonal trajectories

  • Homogeneous equations

  • Integrating factors

  • Reduction of order

2.1 Separable Equations

In this section we shall encounter our first general class of equations with the properties that

  1. We can immediately recognize members of this class of equations.

  2. We have a simple and direct method for (in principle) solving such equations.

This is the class of separable equations.

A first-order ordinary differential equation is separable if it is possible, by elementary algebraic manipulation, to arrange the equation so that all the dependent variables (usually the y variable) are on one side and all the independent ...

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