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