Solve system of nonlinear equations with matlab

how can i solve these 2 nonlinear equations in matlab?

−2𝑥^2+3𝑥𝑦+4sin (y)=6

3𝑥^2−2𝑥𝑦^2+3cos(𝑥)=−4

[Noa Yelin]

Thank's to the answers

Answer 1

[Ameer Hamza]

One way is to use fsolve() from optimization toolbox

fun = @(x, y) [-2*x.^2+3*x.*y+4*sin(y)-6; ...
    3*x.^2-2*x.*y.^2+3*cos(x)+4];

sol = fsolve(@(x) fun(x(1), x(2)), rand(1, 2));
x = sol(1);
y = sol(2);

Result

>> x
x =
    0.5798
>> y
y =
    2.5462

Note: due to periodic functions in you equations, there seems to be multiple solutions.

Another approach is to use vpasolve from symbolic toolbox

syms x y

eq1 = -2*x.^2+3*x.*y+4*sin(y)==6;
eq2 = 3*x.^2-2*x.*y.^2+3*cos(x)==-4;

eq = [eq1; eq2];
sol = vpasolve(eq);
x = sol.x;
y = sol.y;

[Noa Yelin]

so i don't understand.. when I wrote this code-

syms x y
eq1 = -2*x.^2+3*x.*y+4*sin(y)==6;
eq2 = 3*x.^2-2*x.*y.^2+3*cos(x)==-4;
eq = [eq1; eq2];
sol = vpasolve(eq);
x = sol.x;
y = sol.y;

the output i get is -

x =
 
2.5921649161329924198470406781904
 
 
y =
 
2.0411522493463611320382918142382

is this correct?

[Ameer Hamza]

Yes, this is corect. These equations have multiple solutions.