Question

solve the equation dy/dx = y cotx, given x=π/2, y= 1.​

Answer 1

Answer:

The solution of the given equation is y = sin x  

Step-by-step explanation:

Given equation is:

$\frac{dy}{dx}$ = y cot x

=> $\frac{dy}{y}$ = cot x dx

Integrating both sides, we get,

log y = log |sin x| + c                                             --(i)

It is given that at x = $\frac{\pi}{2}$ , y = 1

Therefore, on substituting these values, we get,

log 1 = log |sin $\frac{\pi}{2}$ | + c

=> 0 = 0 + c

=> c = 0

Therefore, equation (i) now becomes,

log y = log |sin x| + 0

=> log y = log |sin x|

Taking antilog both sides,

=> y = sin x  

Therefore, the solution of the given equation is y = sin x  

Answer 2

Answer:

the solution of given eq is y = sinx

Step-by-step explanation:

Given equation is:

= y cot x

=>  = cot x dx

Integrating both sides, we get,

log y = log |sin x| + c                                             --(i)

It is given that at x =  , y = 1

Therefore, on substituting these values, we get,

log 1 = log |sin  | + c

=> 0 = 0 + c

=> c = 0

Therefore, equation (i) now becomes,

log y = log |sin x| + 0

=> log y = log |sin x|

Taking antilog both sides,

=> y = sin x  

Therefore, the solution of the given equation is y = sin x