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Math Help - Calc Help Please!!

  1. #1
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    Calc Help Please!!

    I have a math problem i've been struggling with and staring at it for an hour hasn't helped me. If anyone can help me with it I would be very grateful.

    Right now my class is working on exponential growth and decay. I know that i have to find the integral of both sides and solve for Y but I don't know how to do so exactly.

    Here's the problem:
    if dy/dx=3Y(10-Y)
    integrate to solve for Y
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Kalinator View Post
    I have a math problem i've been struggling with and staring at it for an hour hasn't helped me. If anyone can help me with it I would be very grateful.

    Right now my class is working on exponential growth and decay. I know that i have to find the integral of both sides and solve for Y but I don't know how to do so exactly.

    Here's the problem:
    if dy/dx=3Y(10-Y)
    integrate to solve for Y
    \frac {dy}{dx} = 3y(10 - y)

    \Rightarrow \frac {dy}{y(10 - y)} = 3~dx ......multiplied both sides by \frac {dx}{y(10 - y)}

    using partial fractions on \frac 1{y(10 - y)}, we obtain:

    \frac 1{10} \left( \frac 1y + \frac 1{10 - y} \right)~dy = 3~dx

    now integrate both sides and continue (don't forget your arbitrary constant)
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