## Quick Reference

A differential equation of the form

where *P* and *Q* are given functions. One method of solution is to multiply both sides of the equation by an integrating factor *μ*(*x*), given by

μ(*x*)= exp (∫*P*(*x*) *dx*).

This choice is made because then the left-hand side of the equation becomeswhich is the exact derivative of *μ*(*x*)*y*, and the solution can be found by integration.

In the case where *Q*(*x*)=0, this can also be treated as a separable-variable first-order differential equation.

*Subjects:*
Mathematics.

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