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Solve for intercepts in nonlinear eq

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Sarah Smith
Sarah Smith on 19 Jun 2020
Commented: Ameer Hamza on 19 Jun 2020
This question was flagged by Ameer Hamza
ok

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madhan ravi
madhan ravi on 19 Jun 2020
Hmm nice , knew you would do this. Why waste others time ?
Ameer Hamza
Ameer Hamza on 19 Jun 2020
Original Question:
Title: Solve for intercepts in nonlinear eq
Text: I have these equations and need to solve them in matrix form and find the two intercepts. i was able to do this with linear eq but cant figure it out with nonlinear. my equations are y = 4 - ((x^2)/2) and y/2 = log10(x+8)

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Answers (2)

Ameer Hamza
Ameer Hamza on 19 Jun 2020
This equation does not have a closed-form solution. Therefore, you can solve it using fsolve() or vpssolve() if you have symbolic toolbox since this equation has two solutions. The following code shows a way to get both roots by manually specifying a good initial guess.
syms x y
eq1 = y == 4 - ((x^2)/2);
eq2 = y/2 == log10(x+8);
y1 = solve(eq1, y);
y2 = solve(eq2, y);
eq = y1 == y2;
sol1 = vpasolve(eq, 2)
sol2 = vpasolve(eq, -2)

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Ameer Hamza
Ameer Hamza on 19 Jun 2020
If the solution of four equations exist, the it can be find using following code
syms x y
y1 = 4 - ((x^2)/2);
y2 = 2*log10(x+8);
y3 = x;
y4 = (x+2)/2;
y_sol = vpasolve(std([y1 y2 y3 y4]))
Sarah Smith
Sarah Smith on 19 Jun 2020
I get the error "Empty sym: 0-by-1"
Ameer Hamza
Ameer Hamza on 19 Jun 2020
Which MATLAB release are you using. The symbolic toolbox with R2020a is able to give a solution (y_sol=2). Alternatively, you can try a numerical solver
syms x y
y1 = 4 - ((x^2)/2);
y2 = 2*log10(x+8);
y3 = x;
y4 = (x+2)/2;
y = std([y1 y2 y3 y4]);
fun = matlabFunction(y);
y_sol = fsolve(fun, 0);

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Nipun Agarwal
Nipun Agarwal on 19 Jun 2020
Hey,
You cannot solve Non-linear equations with the Matrix form. Matrix form can be used to solve linear equations only. You need to write your own solver or if you have MATRIX Optimization toolbox installed then you can do it with the help of fsolve. Refer this link for more info on fsolve and its applications.

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