<aside> 🔑 A seperate differential equation is any equation that can be written in the form $y’ = f(x)g(y)$

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• The RH side of the equation can be separated into a function of $x$ times a function of $y$

Separation of Variables

1. Check for any values of $y$ that make $g(y) = 0$
   1. These correspond to constant solutions
2. Rewrite the differential equation in the form $\frac{dy}{g(y)} = f(x)dx$
3. Integrate both sides of the equation
4. Solve the resulting equation for $y$ if possible
5. If an initial condition exists, sub it in and solve for $+C$

Applications

Solution Concentrations

Newton’s Law of Cooling