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Math Help - Need help solving a Diff Equ!!!

  1. #1
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    Question Need help solving a Diff Equ!!!

    I think i am doing it harder that it actually is but i don't know how to solve this. Any help is greatly appreciated.

    Find the general solution of the DE and give the largest interval for which is defined. Are there any transient terms?

    x * dy/dx + 2y = 3


    Thank you!!
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  2. #2
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    Quote Originally Posted by kithy View Post
    I think i am doing it harder that it actually is but i don't know how to solve this. Any help is greatly appreciated.

    Find the general solution of the DE and give the largest interval for which is defined. Are there any transient terms?

    x * dy/dx + 2y = 3


    Thank you!!
    The DE is seperable: \int \frac{dy}{3 - 2y} = \int \frac{dx}{x}.

    Alternatively, you could use the integrating factor method: \frac{dy}{dx} + \frac{2}{x} \, y = \frac{3}{x} and the integrating factor is e^{\int \frac{2}{x} \, dx} = e^{2 \ln |x|} = e^{\ln x^2} = x^2.

    Once you have the solution, the answers to the other questions should become clearer.
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