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Gina

  • 5 years ago

what is the integral of y'sinx=ylny

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  1. amistre64
    • 5 years ago
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    (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
    • 5 years ago
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    thanx very much ;)

  3. amistre64
    • 5 years ago
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    Id like to say youre welcome; but I am not sure if I did it right :)

  4. Gina
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    thanx)

  7. amistre64
    • 5 years ago
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    ... make that: sin(x) needs to have a value greater than 0 :)

  8. Gina
    • 5 years ago
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    ok

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