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Math Help - Need help with a differential equation

  1. #1
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    Need help with a differential equation

    Use the chain rule to find z(s) and z(t) if f(x,y)=x^2y+2xy^3
    x(s,t)=sln(t)
    y(s,t)=s^2+t^3
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  2. #2
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    Re: Need help with a differential equation

    Hey allstar2.

    Can you show us what you have tried? Do you know what the chain rule says?
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  3. #3
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    Re: Need help with a differential equation

    So you want to find z_s and z_t given:
    z=x^2y+2xy^3
    x(s,t)=s\ln{t}
    y(s,t)=s^2+t^3

    Since z depends on both x and y,
    z_s = z_xx_s+z_yy_s
    (treating t as a constant). It's just the chain rule for two variables, except z depends on variables other than s, so you're looking for a partial derivative.

    The situation for z_t is similar.

    That should get you going in the right direction. Post again if you have any more trouble.

    - Hollywood
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