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There is no higher magic necessary, just transcribe into the canonical first-order system, encode the boundary conditions, make a reasonable initial guess of the solution shape and call the BVP solver Pr = 5 def odesys(t,u): F,dF,ddF,θ,dθ = u return [dF, ddF, θ-0.25/Pr*(2*dF*dF-3*F*ddF), dθ, 0.75*F*dθ] def bcs(u0,u1): return [u0[0], u0[1], u1[2]-1, ...


What does differentiating the first equation once to give $\theta'$ and twice for $\theta''$ and plugging into the second equation to give a single equation for $F$ give? Seems like solving a single equation for $F$ might be your best approach (or vice versa).

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