🔵12b – Exact Differential Equations (Solving Exact Differential Equations)

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Mathematics

In this video, we shall study Exact differential Equations and solve two examples.
A differential equation of the form M(x,y)dx + N(x,y)dy = 0 is said to be exact if and only if the partial derivative of My = the partial derivative of Nx;
thus if
My = Nx.

A differential equation of the form M(x,y)dx + N(x,y)dy = 0 is said to be exact if there exist a potential function f(x,y) such that;
df(x,y) = M(x,y)dx + N(x,y)dy……..(1)

since df(x,y) is a function of two variables, its derivative is given by
df(x,y) = (Of/Ox)dx + (Of/Oy)dy……….(2),

hence:
M(x,y) = (Of/Ox) and N(x,y) = (Of/Oy)

Given a differential equation, the first thing to do is to test for exactness. If the differential equation is exact, then you move on to solve to find the general solution to the exact differential equation.

The solution of an exact differential equation must be of the form; f(x,y) = c, where c is a constant.

In this lesson we shall solve two major examples

00:00 – Ex 3
08:49 – Ex 4

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