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P4 Second Order Differential Equations Question watch

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    Find the general solution of

    x d2y - 2 dy + x = 0
    dx2 dx

    Using the substitution dy/dx = v

    (Heinemann P4 textbook, Ex6E, Q7)

    Any takers?
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    im gonna try it now... might take a little while though... so if someone hasn't posted their answer i will post mine soon
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    I tried and failed - sorry!
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    ok i think i got it... but i left the book downstairs... is the answer:
    y=(x^2)/2 + Ax^3 +B

    forgot to check before
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    (Original post by S1M)
    ok i think i got it... but i left the book downstairs... is the answer:
    y=(x^2)/2 + Ax^3 +B

    forgot to check before
    Hooray! Now could you please enlighten me as to how you did it, because I don't have a clue!
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    ok this might take some time...

    dy/dx=v
    d2y/dx2 = dv/dx
    substitute that into eqn

    xdv/dx - 2v + x = 0

    divide by c

    dv/dx -2v/x +x/x = 0

    dv/dx + (- 2/x)v = -1

    IF = e^(int of -2/x) = e ^ (-2lnx) = e ^ (ln(x^-2))

    then from there its just like 1st order
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    ok ill finish it off for ya...

    v/x^2 = int 1/x^2
    = 1/x + C
    then sub back v = dy/dx

    rearrange
    dy/dx = x + Cx^2
    intergrate:
    y = (x^2)/2 + (C/3)x^3 + B
    C/3 = A
    and you must be able to do the last step
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    (Original post by S1M)
    ok this might take some time...

    dv/dx -2v/x +x/x = 0

    dv/dx + (- 2/x)v = 1
    Shouldn't that be -1?
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    geehhh I'm stupid - I forgot the +c when I integrated the -1/x^2. Talk about dumb...

    Cheers S1M, rep cometh your way!
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    (Original post by shift3)
    Shouldn't that be -1?
    yup -1... was just a typo when copying it from paper...
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    (Original post by flyinghorse)
    geehhh I'm stupid - I forgot the +c when I integrated the -1/x^2. Talk about dumb...

    Cheers S1M, rep cometh your way!
    Your welcome... thanks for the rep
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    well i was nearly there


    i just forgot to integrate to get y = ... :rolleyes: thanks anyway thats good work!
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    (Original post by kikzen)
    well i was nearly there


    i just forgot to integrate to get y = ... :rolleyes: thanks anyway thats good work!
    no problem... thanks for the rep
 
 
 
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Updated: June 26, 2004

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