Differential equation introduction | First order differential equations | Khan Academy

Differential equations, a tourist's guide | DE1

<aside> ✅ An ordinary differential equation is an equation involving an unknown function (e.g $y(t)$) and one or more of its derivatives

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Examples of Diffrential Equations

• Equation for radioactive decay $y’ = -ky$ that models the amount of Carbon-14 in a fossil
• Newton’s Second Law of a body experiencing a time-varying force $F(t) = mx’’(t)$
• Equation for charge $Q(t)$ in an RLC circuit $LQ’’(t) + RQ’(t) +\frac{1}{c}Q(t) = 0$

Equilibrium Solutions

<aside> ☝ An equilibrium solution to a differential equation is a solution $y(t)$ to that equation that also happens to be a constant function

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• Solution of the form $(y)t = c$ where $c$ is constant
• Set differential equation $y’ = 0$ and then solve for $y$
• General solution is in terms of $y(t)$, whereas the particular solution is in terms of $y(t_0)$, where $t_0$ is an initial condition
• $y’ = f(y)$