Solve for intercepts in nonlinear eq

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Sarah Smith
Sarah Smith 2020-6-19
评论： Rena Berman 2020-10-12
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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Ameer Hamza
Ameer Hamza 2020-6-19
Original Question:
Name: Hannah Bartholomew
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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回答（2 个）

Ameer Hamza
Ameer Hamza 2020-6-19
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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Sarah Smith
Sarah Smith 2020-6-19
I get the error "Empty sym: 0-by-1"
Ameer Hamza
Ameer Hamza 2020-6-19
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 2020-6-19
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.
https://in.mathworks.com/help/optim/ug/fsolve.html

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