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Math Help - Singular Points

  1. #1
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    Singular Points

    Need help with solving this question i have no idea how to even start so any help would be appreciated thanks

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  2. #2
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    Why not just start by solving the DE:

    y'\pm\frac{2}{x}y=3

    via integrating factor and obtain the two solutions. What can you say about either solution at x=0?
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  3. #3
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    Quote Originally Posted by shawsend View Post
    Why not just start by solving the DE:

    y'\pm\frac{2}{x}y=3

    via integrating factor and obtain the two solutions. What can you say about either solution at x=0?
    y do i need to solve that DE ? thats just the example in question i think i need to solve the DE in part a) which i dont knw how to
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  4. #4
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    Ok, then here's how I'd do (A):

    xy'+2y=3x,\quad y(0)=y_0 and dividing by x:

    y'+2/x y=3 for which the integrating factor is x^2 so we have:

    x^2(y'+2/x  y)=3x^2 which the left side is the differential of x^2y so:

    \int d(x^2y)=\int 3x^2 or:

    y(x)=x+\frac{c}{x^2} and if y_0=0 then I can let c=0 and obtain the solution y=x. However, if y_0\neq 0 say 3 for example, then I'd obtain 3=0+\frac{c}{0} which has no solution.

    Ok, so I'm a little uneasy about dividing through by x in the first step since this is valid if x\ne 0 then obtain the solution and solve it for x=0.
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