Solving first order differential equation: Method 1 (sect. 2.2): Separate variables. Method 2 (sect. 2.1): If linear [y′(t)+p(t)y(t) = g(t)], multiply equation by an integrating factor u(t) = e^{∫ p(t)dt}.

y′ + py = g

y′u + upy = ug

(uy)′ = ug

∫ (uy)′ = ∫ ug

uy = ∫ ug etc...

Method 3 (sect. 2.4): Solve Bernoulli’s equation, y′ + p(t)y = g(t)y^{n},

when n > 1 by changing it to a linear equation by substituting v = y^{1−n} If v = \frac{dx}{dt}, can use the following to simplify (especially if there are 3 variables).

\frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt} = v \frac{dv}{dx}