What does the Standard Error in Non Linear Model Fit signify ? How is it calculated ? How can I interpret the value in terms of goodness of my fit ?

# Tag: nonliner

## export – Non-liner equation – Mathematica Stack Exchange

Mathematica cannot solve your equation for X .

Instead try to solve it for t

```
sol=Solve(X (X - a) + b Exp(-2 X t) == B, t )((1)) /. C(1) -> 0(*forces real solution*)
(*{t -> Log(b/(B + a X - X^2))/(2 X)}*)
```

Now you know t as a function of X.

For examplary parameters you can plot the result

```
ParametricPlot({t, X} /. sol /. {a -> 1/5, b -> 1, B -> 3/2}, {X, -2,2}, AxesLabel -> {t, X})
```

## nonlinear – Got Solutions to a set of non-liner equations in Matlab but not in Mathematica. Why?

I was trying to solve a set of nonlinear equations using NSolve in mathematics. I got a result saying that no solution ({}). My friend tried it in Matlab, he was able to get a solution to the same set of equations for the same given parameters. Now I doubt who to trust?

I add my functions below

```
ClearAll(Evaluate(StringJoin(Context(), "*")))
Needs("Utilities`CleanSlate`");
CleanSlate();
ClearInOut();
d(xt_, xv_, xo_, xb_) := (1189*(3*xv^2*(8/5 + xt/10) + (6*xv*xt*xo)/5 +
(6/5 - xt/10)*xo^2)*Cos(xb)^3)/3000000;
ma1(xt_, xv_, xo_, xb_) := (1189*((48*xv^2)/5 + (3*xv^2*xt)/5 +
(16*xv*xt*xo)/5 + (18*xo^2)/5 - (3*xt*xo^2)/10)*Cos(xb)^2)/48000000;
ma2(xt_, xv_, xo_, xb_) := (5/4)*xo^2*Cos(xb)*Sin(xb);
q1(xt_, xv_, xo_, xb_) := (1189*(3*xt*((16*xv^2)/5 + (6*xo^2)/5) +
(1/10)*(-6*xv^2 - 16*xv*xt*xo + 3*xo^2))*Cos(xb)^3)/48000000;
f11(xt_) := NSolve({q1(xt, xv, xo, xb) == 0 &&
d(xt, xv, xo, xb) - 133.05 == 0 &&
ma1(xt, xv, xo, xb) - ma2(xt, xv, xo, xb) == 0}, {xv, xo, xb}, Reals,
WorkingPrecision -> 5)
f11(0.01)
```

kindly someone help me

In Matlab, he obtained these values xv = 232.9328, xo = 290.8831, xb = 1.7934 10 ^ (- 4); And the accuracy of solutions was up to 5 digits in matlab