The equation is exact, as we have seen. If we expand the left-hand side of this equation (i.e. differentiate the product) we obtain
Hence the equation
must be exact, but it is not so obvious that it is exact as in the original form. This leads to the following Key Point:
Solve the equation
Comparing this equation with the form in Key Point 3 we see that and . Hence the equation can be written
which has solution
Solve the equation .
You should obtain since, here and . Then
- Solve the equation
- Solve the equation given the condition
- Solve the equation .
- Show that the equation is exact and obtain its solution.
Show that the equation
is not exact.
Multiply the equation by and show that the resulting equation is exact and obtain its solution.