Find the solution of the problem (1 3. (2 cos x - y sin x)dx + (cos x + sin y)dy=0.

Step-by-step explanation:

Let:

This is an exact differential equation because:

With this in mind let's define f(x,y) such that:

and

So, the solution will be given by f(x,y)=C1, C1=arbitrary constant

Now, integrate with respect to x in order to find f(x,y)

where g(y) is an arbitrary function of y

Let's differentiate f(x,y) with respect to y in order to find g(y):

Now, let's replace the previous result into :

Solving for

Integrating both sides with respect to y:

Replacing this result into f(x,y)

Finally the solution is f(x,y)=C1 :

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