Dx + (x cot y+ sin y)dy=0 ,solve the de

Multiply both sides by :

The ODE is now exact, since

so there exists a solution of the form . This solution satisfies

Integrating both sides of the first PDE wrt gives

and differentiating wrt gives

So the ODE has solution

which can be rewritten and simplified as

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .