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Math Help - Help me ! A function satisfies the differential equation

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    Angry MOD can delete this topic

    \frac{dy}{dt}= y^{4}-6y^{3}+5y^{2}

    a. What are the constant solutions of the equation?
    b. For what values of x is y increasing?
    c. For what values of x is y decreasing?
    Last edited by mr fantastic; February 23rd 2009 at 01:02 AM. Reason: Restored question that was deleted by the OP
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    Quote Originally Posted by butbi9x View Post
    \frac{dy}{dt}= y^{4}-6y^{3}+5y^{2}

    a. What are the constant solutions of the equation?
    b. For what values of t is y increasing?
    c. For what values of t is y decreasing?
    Should be t (in red)

    a. If y=a, where a is a constant, then \frac{dy}{dt}=0
    So solve for a in :
    a^4-6a^3+5a^2=0
    0=a^2(a^2-6a+5)=a^2(a-1)(a-5)
    So y=0, y=1 and y=5 are the constant solutions to the equations.

    b. If y is increasing, it means that \frac{dy}{dt}>0
    So find the values (I guess they should still be constant), such that y^4-6y^3+5y^2>0 \Leftrightarrow y^2-6y+5>0

    Same thing for c. : if y is decreasing, \frac{dy}{dt}<0
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