DSolve[{(k+kTanh[(Sqrt[k]x)/(2Sqrt[Dm])]-kTanh[(Sqrt[k]x)/(2Sqrt[Dm])]^2)*(W1[x]-2*W2[x]/R0)+Dm*D[W1[x],{x,2}]0,(Dc*k*R0/(4*Dm))*((1+Tanh[(Sqrt[k]x)/(2Sqrt[Dm])])^2)*(W1[x]-2*W2[x]/R0)+Dc*D[W2[x],{x,2}]0},{W1[x],W2[x]},x]