I am trying to solve numerically a difficult implicit equation and plot the solution. The thing that I want to solve numerically is the following:
$$ Q(h)=\frac{0.13}{1-10^{-4}\log{\frac{Y(h)}{100}}} $$
$$ P(h)=2*10^{4}*\sqrt{\frac{1}{1-10^{-4}\log{\frac{Y(h)}{100}}}}-1/6$$
$$ Y(h)=\sqrt{3*Q(h)*h^2-(P(h)+1/6)*10^{12}} $$
So the point is that I want to solve (numerically is the only way) the implicit equation of Y(h) in terms of h, but note that functions Q(h) and P(h) also depend on Y (so implicitly on h).
I want to get numerically the solution of Y(h) in order to use this to plot Q(h) and P(h) in terms of h.
Someone knows how to do this??? Thanks!
Expressions in format code:
Q[h_] := 0.13/(1 - 10^(-4)*Log[Y[h]/100]);
P[h_] := 2*(10^4)*Sqrt[1/(1 - 10^(-4)*Log[Y[h]/100])] - 1/6;
Y[h_] := Sqrt[3*Q[h]*h^2 - (P[h] + 1/6)*10^12];