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Math Help - differential equations urgent homework!

  1. #1
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    differential equations urgent homework!

    Solve the differential equation y’ = y/x using the separation of variables
    a. separate the variables in y’ = y/x
    b. use integration to solve your equation from step a.

    find the general solution of the differential equation (x^2 + 5)dy = xydx by completing the steps below.
    a. separate the variables
    b. integrate the resulting equation
    c. solve for y
    d. check by differentiation
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  2. #2
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    Hi again,

    as I've told you:
    dy/dx = y/x --> y*dy = x*dx
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  3. #3
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    the problem is my teacher doesnt teach me anything so i dont know how to integrate or do any of this do you mind explaining further into the problem
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  4. #4
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    Ooops, I miscalculated:

    dy / dx = y / x --> dy / y = dx / x
    \int x dx = ln(x) + C
    \int y dy = ln(y)
    So ln(y) = ln(x) + C
    so
    y = exp(ln(x)+C) = D*x
    D is constant.

    controling:
    dy / dx = D
    and
    y / x = D
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  5. #5
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    Quote Originally Posted by Skalkaz View Post
    Ooops, I miscalculated:

    dy / dx = y / x --> dy / y = dx / x
    \int {\color{red}\frac{1}{x}} \, dx = ln(x) + C
    \int {\color{red}\frac{1}{y}} \,  dy = ln(y)
    So ln(y) = ln(x) + C
    so
    y = exp(ln(x)+C) = D*x
    D is constant.

    controling:
    dy / dx = D
    and
    y / x = D
    Please note the corrections (in red).
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