Clifland

2021-03-05

Give the correct answer and solve the given equation $dx+(\frac{x}{y}-\mathrm{sin}y)dy=0$

brawnyN

Skilled2021-03-06Added 91 answers

Multiply this equation by y:

Now we will try to find a function F:

and

Start with

and integrate with respect to x:

where C(y) is a constant with respect to x (an integrating constant!). From (2)

Using (1) now, we get that

Thus,

where D is a constant.

Therefore,

Now the solution of the initial differential equation is given by

so

where C is some constant.

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