First Order Differential Equations with Constant Coefficients

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Encyclopedia>Functions>Differential Equations>First Order>How to Solve First Order Differential Equations with Constant Coefficients

A differential equation of the type $y^{'} + a y = b$ can be solved by using integrating factors. This works because constants can also be functions. Since they are constants, you can use the following formula to speed up the process:

y = \frac{b}{a} + C \cdot e^{- a x}

Example 1

Solve the differential equation $y^{'} - 3 y = 6$

Insert the coefficients into the formula and you get

y = \frac{6}{- 3} + C \cdot e^{3 x} = - 2 + C e^{3 x}

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What Are First Order Differential Equations?

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How to Solve First Order Differential Equations with Initial Conditions