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Math Help - [SOLVED] first order equation

  1. #1
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    [SOLVED] first order equation

    Hello,
    I have to solve such equation:
    y'-y+y^2e^{2x}=0
    I thought about two substitutions. First t=1/y, and after that t=uv, but after doing that lot of calculations I still do not get right result. Is there any faster and more reliable method?
    V.
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by Vermax View Post
    Hello,
    I have to solve such equation:
    y'-y+y^2e^{2x}=0
    I thought about two substitutions. First t=1/y, and after that t=uv, but after doing that lot of calculations I still do not get right result. Is there any faster and more reliable method?
    V.
    This is a Bernoulli equation:
    \frac {dy}{dx} + P(x) y = Q(x) y^n

    where P(x) = -1 and Q(x) = -e^{2x} and n=2.

    Putting t = 1/y is the substitution you want. Then you should be able to put it in the form:

    \frac {dt}{dx} = (1-n) P(x) t = (1-n) Q(x)

    where P, Q, t are as above.

    You should then be able to solve it using an integrating factor, I expect.
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  3. #3
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    Just wanted to thank you for your answer and confirmation. Equation solved
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