Question

solve this:-f(x)dx+g(y)dy=0​

Answer 1

Answer:

An exact equation is in the form

f(x) dx + g(y) dy = 0

and, has the property that

dx f = dy g

(If the differential equation does not have this property then we can't proceed any further).

As a result of this, if we have an exact equation then there exists a function h(x, y) such that

Dy h = f and Dx h = g

So then the solutions are in the form

h(x, y) = c

by using the fact of the total differential. We can find then h(x, y) by integration and thus prove:

f(x)dx+g(y)dy=0