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The homogeneous equation....how to solve? might require the use of greens function? watch

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    The homogeneous equation:

    y''[x] + p[x]y'[x] + q[x]y[x] = 0

    is subject to the inhomogeneous boundary conditions
    y[a] = (alpha)
    y[b] = (beta)
    considering a transformation y[x] = Y[x] + P[x],
    where P[x] is a suitablly chosen (simple) polynomial,

    show how this problem can be transformed into one for Y[x] with homogeneous boundary conditions but where Y[x] satisfies an inhomogeneous equation.

    have a go......
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    P must be such that Y(a) = Y(b) = 0. So we need P(a) = alpha and P(b) = beta. Those conditions are satisfied if

    P(x) = alpha + (beta - alpha)(x - a)/(b - a)

    --

    Substituting y(x) = Y(x) + alpha + (beta - alpha)(x - a)/(b - a) into

    y''(x) + p(x)y'(x) + q(x)y(x) = 0

    gives

    Y''(x) + p(x)[Y'(x) + (beta - alpha)/(b - a)] + q(x)[Y(x) + alpha + (beta - alpha)(x - a)/(b - a)] = 0

    Y''(x) + p(x)Y'(x) + q(x)Y(x) = -[(beta - alpha)/(b - a)][p(x) + q(x)(x - a)] - alpha q(x)
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    cheers m8

    really weird thing, i havn't used these forums in ages...let alone give out much rep. but you were the last person i repped so i got to rep a random person first....bla bla.

    n e way thx
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    what is rep?
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    http://www.thestudentroom.co.uk/faq....repu#faq_reput
 
 
 
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