## Gina 5 years ago what is the integral of y'sinx=ylny

1. amistre64

(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) ?

2. Gina

thanx very much ;)

3. amistre64

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

4. Gina

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?

5. amistre64

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.

6. Gina

thanx)

7. amistre64

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

8. Gina

ok