I am trying to use the ODE Analyzer tool in order to solve a system of differential equations, and then add the plot of a polynomial function to the plot generated using the ODE Analyzer tool.
I have successfully figured out how to use the ODE analyzer to produce the plot of the solution curve:
Here's the system of DE's:
diff(f(x), x) = u(x)
diff(u(x), x) = x + f(x) - f(x)^2
Initial conditions: f(0) = -1, u(0) = 1
The code for the solution curve is given by the ODE Analyzer as follows:
sol1 := dsolve([diff(f(x), x) = u(x), diff(u(x), x) = x + f(x) - f(x)^2, f(0) = -1, u(0) = 1], numeric, method = taylorseries[series]);
plots[odeplot](sol1, [x, f(x)], 0 .. 10, color = red);
Does anyone know how I might add an additional plot to compare to the plot the ODE Analyzer produced?
The plot I would like to add is: T(x) = -1 + x - x^2 +2/3*x^3 - 1/3*x^4 + 1/5*x^5