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Math Help - Differential equation

  1. #1
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    Differential equation

    i) In the differential equation [1-(y^2)](dy/dx)+1/y=e^(2x)

    make the substitution u=1/y and hence show that the general solution to the equation is y=1/[(Ae^x)-e^(2x)].

    Help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by free_to_fly View Post
    i) In the differential equation [1-(y^2)](dy/dx)+1/y=e^(2x)

    make the substitution u=1/y and hence show that the general solution to the equation is y=1/[(Ae^x)-e^(2x)].

    Help would be greatly appreciated.
    You can bring this differencial equation to an exact differencial equation by an integrating factor.

    Write,
    (1/y-e^x)+(1-y^2)y'=0
    And let,
    M(x,y)=1/y-e^x
    N(x,y)=1-y^2

    Note the cross partial test fails,
    M_y not = N_x

    But,
    (M_y-N_x)/N
    Is a function only of "y" thus, you can find an integrating factor.
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