Math, asked by srivangapandu, 9 months ago



The solution of cos y dy+ (x sin y - 1) dx = 0 is​

Answers

Answered by yashivishwakarma
0

Answer:

Hi,

Start like this,

let, x+y = t

dt/dx = 1 + dy/dx ………….I

or, dt = dx + dy…………….II

now, dy/dx = cosx*cosy - sinx*siny

dy/dx = cos(x+y)

dt/dx - 1 = cos(t) ……… from I

dt/(1+cost) = dx

on the left side multiply nd divide by (1- cost)… rationalize.

(1- cost)/sin^2(t) dt = dx

dt/sin^2(t) - cost dt/sin^2(t) = dx

cosec^2(t) dt - cot(t)cosec(t) dt = dx

integrating both sides,

-cot(t) + cosec(t) + c = x

-cot(x+y) + cosec(x+y) + c = x

Hope this clarifies,

Thanks

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 · Answer requested by Kamlesh Siroya

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Other Answers

Bhavit Sharma, Undergrad, Computer Science and Engineering.

Answered September 5, 2015

Originally Answered: dy/dx=cosx*cosy-sinx*siny? Solve this problem

Dy/dx = cos(X+Y)

Take (X+Y) = t.

Differentiate on both sides.

DT/dx - 1 = dy/dx ----equation 2

Then put equation 2 in 1st equation,

dt/dx = 1 + cost

Now find the solution of this equation as it's very trivial.

And replace 't' by X+Y finally. And you're done.

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