I have a model like this:
$$ Y=B_0 + B_1x_1^2 + B_2x_2e^{B_3x_2} + B_4x_3+B_5x_3^2+c $$ Is it a linear model? How can I understand the linear and non-linear model of regression? Sometimes I found some model as a linear which contains non-linear terms.
I suppose that you have $n$ data points $(x_{1i},x_{2i},x_{3i},Y_i)$ and you want to adjust, for a good fit, the parameters $B_0,B_1,B_2,B_3,B_4,B_5$ which appear in the model $$Y=B_0 + B_1x_1^2 + B_2x_2e^{B_3x_2} + B_4x_3+B_5x_3^2$$
The model is linear when the derivative of $Y$ does not depend on any parameter. This is the case here except for $B_3$. So, if you fix $B_3$ to any value, the model is fully linear. If you do not, then the model is nonlinear and you need nonlinear regression; this implies that you provide "good" starting values.
One way to do it is to make, in a preliminary step, the model linear. Give $B_3$ a value; run the linear regression and compute the sum of squares $SSQ$ (which is a function of $B_3$). Change the value given to $B_3$ until you find an area where $SSQ$ is showing a minimum value; at this point, you have your guesses. For sure, the best is to plot $SSQ$ as a function of $B_3$.