The solution is obtained and validated by an existence and uniqueness theorem for the following nonlinear boundary value problem ddx1+δy+γy2ndydx+2xdydx=0,x>0,y(0)=0,y(∞)=1,$$ frac{d}{dx}left{left(1#x0002B;delta y#x0002B;gamma {y}#x0005E;2right)}#x0005E;nfrac{dy}{dx}right#x0002B;2xfrac{dy}{dx}#x0003D;0,x0,y(0)#x0003D;0,yleft(infty right)#x0003D;1, $$ which was proposed in 1974 by Cho and Sunderland to represent a Stefan problem with a nonlinear temperature‐dependent thermal conductivity on the semi‐infinite line (0,∞)$$ left(0,infty right) $$. The modified error function of two parameters φδ,γ$$ {varphi}_{delta, gamma } $$ is introduced to represent the solution of the problem above, and some properties of the function are established. This generalizes the results obtained in earlier studies.
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