I want to solve the system of non-linear differential equations given below numerically.
$$y''(t)+500y'(t)+100y(t)=-33\cos(500t)-66\cos(1000t)$$ $$300x'(t)=1000y(t)+500y'(t)-35\tanh(50x'(t))$$
Notice that there is a derivative of $x$ inside $\tanh$. I tried the code below, but many errors appeared.
sol1 =
NDSolve[{y''[t] + 500 y'[t] + 100 y[t] == -33 Cos[500 t] - 66 Cos[1000 t],
y[0] == 0, y'[0] == 0}, y, {t, 0, 30}];
sol2 =
NDSolve[{300 x'[t] ==
1000 First[Evaluate[y[t] /. sol1]] + 500 First[Evaluate[y'[t] /. sol1]] -
35 Tanh[50 x'[t]], x[0] == 0}, x, {t, 0, 30}];
Plot[{Evaluate[x[t] /. sol1], Evaluate[y[t] /. sol2]}, {t, 0, 30}, PlotRange -> All]
How can I solve my system of differential equations using Mathematica?
Edit
I found the answer! thanks to Nasser. The solution for $x(t)$ is like below. I just need to adjust the axis