Question

what is the integral of y'sinx=ylny

Answer 1

(dy/dx)(sin(x)) = y ln(y)
(dy) sin(x) = y ln(y) (dx)
(S) (dy)/(y ln(y)) = (S) (dx)(sin(x))

ln(y ln(y)) = ln(sin(x)) +C ; sin(x) needs a restriction. sin(x) > 0?
ln(y ln(y)) = ln(sin(x)) +C

(ln(y ln(y)) could split to = ln(y) + ln(ln(y)); would that
be more helpful?)

ln(y) +ln(ln(y)) = ln(sin(x)) +C

ln(y) +ln(ln(y)) = e^(sin(x)) + e^C
y +ln(y) = e^(Csin(x))
y= [e^(Csin(x))]- ln(y) ?

Answer 2

thanx very much ;)

Answer 3

Id like to say youre welcome; but I am not sure if I did it right :)

Answer 4

but on this stage i did not understand clear cud you explain? ln(y ln(y)) = ln(sin(x)) +C ; sin(x) needs a restriction. sin(x) > 0?

Answer 5

the domian of the Ln(x) function is all value of x>0. The graph of the Ln function never touches 0 so we have to limit the input values for ln(sin(x)) to make any sense. sin(x) needs to have a value of 0 or greater.

Answer 6

thanx)

Answer 7

... make that: sin(x) needs to have a value greater than 0 :)

Answer 8

ok