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Math Help - [SOLVED] differential equations

  1. #1
    Member ronaldo_07's Avatar
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    [SOLVED] differential equations

    Compute the general solution of the linear inhomogeneous differential equation y' = \frac{-y}{1 + x}+ 3x .
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  2. #2
    Member ronaldo_07's Avatar
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    I fond the ingegrating factor to be 1+x and now I dont know where do to from there
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  3. #3
    Member ronaldo_07's Avatar
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    I solved it to be y= \frac{\frac{3x^2}{2}+x^3 +C}{1+x}
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  4. #4
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    It doesn't help to find the integrating factor if you don't know what an "integrating factor" is! Don't memorize formulas, learn concepts!

    An integrating factor for a linear differential equation of the form dy/dx+P(x)y= f(x,y) is a function of x, \mu(x) such that multiplying both sides of the equation by it converts the left side into a "perfect" derivative so that the equation becomes: \mu(x)dy/dx+ \mu(x)P(x)y= \frac{d(\mu(x)y)}{dx}= \mu(x)f(x,y).

    If (1+ x) really is an integrating equation (I haven't checked that) then multiplying 1+x on both sides converts the equation \frac{dy}{dx}+ \frac{1}{1+ x} y= 3x to \frac{d((1+x)y}{dx}= 3x((x+1). Now integrate both sides with respect to x.
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