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Math Help - I need help with this differential equation

  1. #1
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    I need help with this differential equation

    u''+u'/z=(K*g/q^2*z+T*K/q^2*z^2)*u
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  2. #2
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    Quote Originally Posted by Emilly View Post
    u''+u'/z=(K*g/q^2*z+T*K/q^2*z^2)*u
    For clarification, is your ODE

     <br />
u'' + \frac{u'}{z} - \left(\frac{K\,g}{q^2 z} + \frac{T\,K}{q^2 z^2} \right) u = 0<br />
?
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    yes
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  4. #4
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    Quote Originally Posted by Danny View Post
    For clarification, is your ODE

     <br />
u'' + \frac{u'}{z} - \left(\frac{K\,g}{q^2 z} + \frac{T\,K}{q^2 z^2} \right) u = 0<br />
?
    First let a = \frac{K\,g}{q^2} and b = \frac{T\,K}{q^2} so your ODE is

     <br />
z^2 u'' + z u' -(a z+b)u = 0<br />

    Under the transformation z = \frac{x^2}{4a} this ODE becomes

    x^2 u'' + x u' - (x^2 + 4b)u= 0 a modified Bessel equation which has standards solutions.
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