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Differential Equations Help, non-linear first order with substitution

  1. Sep 16, 2014 #1
    (r^2) (dT/dr)+B*r*T=T^2, with initial condition dT/dr |r=0 =0 where B is a constant

    I've gotten it to this:

    dT/dr = -BT/r + T2 / r2

    by dividing everything by r2, then I substitute using λ= T/r which gives:

    r * dλ/dr + lambda = -B * (λ) + λ^2

    I don't know how to separate from here, any help is appreciated
  2. jcsd
  3. Sep 17, 2014 #2
    Aren't you almost finished?

    ## r \frac{d\lambda}{dr} + \lambda = -B\lambda + \lambda^{2} \Rightarrow \frac{1}{-\lambda(B+1) + \lambda^{2}} \frac{d\lambda}{dr} = \frac{1}{r} ##
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