Question

. Solve the differential equation
(cos x cos y - cot x) dx - (sin x sin y) dy = 0.​

Answer 1

Answer:

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Step-by-step explanation:

I assume that the second y in the dy term is a misprint in the differential form making it into an exact differential. If so, then M=cos(x)cos(y)−cot(x) and N=−sin(x)sin(y).

Note that My=−cos(x)sin(y) and Nx=−cos(x)sin(y) also. This implies that there is a function F(x,y) such that

Fx=M=cos(x)cos(y)−cot(x) and Fy=N=−sin(x)sin(y).

Integrating we see that F(x,y)=sin(x)cos(y)−ln(sin(x)) is the integral of this differential form. That is,  dF=Mdx+Ndy