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Separation of Variables watch

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    Hi, I'm struggling with a separating the variables problem.

    First, I make the equation 1/(y+5) dy = e^x dx
    Then, I integrate to get ln(y+5)=e^x + c
    Then, I raise by e^x to get y+5=e^(e^x+c)
    Then simply rearrange to get y=e^(e^x+c)-5.

    Have I gone wrong anywhere or can I simplify, or is it just this same test site being stupid.

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    (Original post by Substitution)
    Hi, I'm struggling with a separating the variables problem.

    First, I make the equation 1/(y+5) dy = e^x dx
    Then, I integrate to get ln(y+5)=e^x + c
    Then, I raise by e^x to get y+5=e^(e^x+c)
    Then simply rearrange to get y=e^(e^x+c)-5.

    Have I gone wrong anywhere or can I simplify, or is it just this same test site being stupid.

    Thanks
    Looks fine, but you might want to write is as y = Ae^{e^x} -5 instead.
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    (Original post by Zacken)
    Looks fine, but you might want to write is as y = Ae^{e^x} -5 instead.
    That's what I thought, but the question says to use c so I left it as is.

    Thanks
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    (Original post by Substitution)
    That's what I thought, but the question says to use c so I left it as is.

    Thanks
    Maybe y = e^ce^{e^x} - 5 then? But it shouldn't make much of a difference.
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    (Original post by Zacken)
    Maybe y = e^ce^{e^x} - 5 then? But it shouldn't make much of a difference.
    I'll try and enter it as that tomorrow, not feeling confident about the fact were going to be using this site for our tests on monday!
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    Perhaps try  y = ce^{e^x} -5 also, i.e. what Zacken said but use c as it asks.
 
 
 
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