Solve for intercepts in nonlinear eq

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)

[madhan ravi]

Hmm nice , knew you would do this. Why waste others time ?

[Ameer Hamza]

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)

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Ameer Hamza]

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)

[Sarah Smith]

Thank you!! do you know how i would do this if i wanted to solve for the intersection of the those equaitions but also y = x and y = (x+2)/2? So 4 equations total for a the solution

[Ameer Hamza]

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]

I get the error "Empty sym: 0-by-1"

[Ameer Hamza]

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);

Answer 2

[Nipun Agarwal]

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