Using an Integrating Factor to Solve a Separable Equation
Drag the locator to change the initial condition in the autonomous equation or move the sliders for and . (An autonomous equation is one where the independent variable—here —does not appear explicitly; i.e., and are independent of .) In this case the integrating factor is determined by the constant and the solution at infinity is determined by the constant .
This example comes from [1], Section 2.1, Modeling with First Order Equations.
Reference
[1] J. R. Brannan and W. E. Boyce, Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications, New York: John Wiley and Sons, 2010.
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