Question

Solve the differential equation : `"x"(d"y")/(d"x") + "y" - "x" + "xy"cot"x" = 0; "x" != 0.`

Answer 1

`x dy/dx + y - x + xy cos x = 0`

⇒ `dy/dx + (1/x + cot x ) y = 1`

I.F. = `e^(int(1/x + cot x) dx) = e^(log(x sin x))`

= x sin x

`∴ y xx  x sin x = x sinx dx`

⇒ xy sin x = - x cos x + sin x + C