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How to Solve Exact First Order Differential Equations

A differential equation is exact if you can integrate the right-hand side and the left-hand side directly. This is the simplest type of differential equations.

Rule

Exact Differential Equations

y = f(x) y =f(x)dx + C

Example 1

Solve the differential equation y = 1 x + 2x

y =ydx = 1 x + 2xdx = ln |x| + x2 + C

y =ydx = 1 x + 2xdx = ln |x| + x2 + C

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How to Solve First Order Differential Equations with Initial Conditions
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