<aside> 🐋 A first order differential equation is linear if it can be written in the form $a(x)y’ + b(x)y=c(x)$

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Standard Form

Equation when it is in the form $y’ + p(x)y = q(x)$

Integrating Factors

1. Put the equation into standard form and identity $p(x)$ and $q(x)$
2. Calculate the integrating factor $\mu(x) = e^{\int p(x)dx}$
3. Multiply both sides of the differential equation by $\mu(x)$
4. Integrate both sides of the equation obtained in step 3, and divide both sides by $\mu (x)$
5. If there is an initial condition, determine the value of $C$

Applications