In the last lesson about linear differential equations, all the general solutions we found contained a constant of integration, C. But we’re often interested in finding a value for C in order to generate a particular solution for the differential equation. This applies to linear differential equations, but also to any other form of differential equation. The information we’ll need in order to find C is an initial condition, which is the value of the solution at a specific point.
Read MoreTo investigate first order differential equations, we’ll start by looking at equations given in a few very specific forms. The first of these is a first order linear differential equation. First order linear differential equations are equations given in the form dy/dx+P(x)y=Q(x).
Read MoreWhereas partial derivatives are indicated with the “partial symbol,” we never see this notation when we’re dealing with ordinary derivatives. That’s because an ordinary derivative is the derivative of a function in a single variable. Because there’s only one variable, there’s no need to indicate the partial derivative for one variable versus another.
Read MoreWe already know how to find the general solution to a linear differential equation. But this solution includes the ambiguous constant of integration C. If we want to find a specific value for C, and therefore a specific solution to the linear differential equation, then we’ll need an initial condition, like f(0)=a. Given this additional piece of information, we’ll be able to find a value for C and solve for the specific solution.
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