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How to Solve First Order Differential Equations with Constant Coefficients

A differential equation of the type y + ay = 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 = b a + C eax

Example 1

Solve the differential equation y 3y = 6

Insert the coefficients into the formula and you get

y = 6 3 + C e3x = 2 + Ce3x

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How to Solve First Order Differential Equations with Initial Conditions