finding the roots of a multivariable equation

how would i go about plotting the roots (y) of a multivariable equation:

ysin(2x) + sin(2yx) = 0

with x values of pi/2 to pi?

i'm looking for the smallest non-zero, non-negative root

this is what i have so far:

x=linspace(pi/2,pi)
for z=(1:100)
    eqn= @(y) y*sin(2*x(z)) + sin(2*y*x(z))
    yRoots = fzero(eqn,0)
end

my yRoots is just an array of 0's in this case. for example, for x=pi/2 , the root i'm actually looking for is 1. how do i get matlab to ignore the 0 root and just give me the first positive root?

[David Hill]

You may want to try plotting first. You will need to change the search interval to find the root you want.

y=-20:.1:20;
z=arrayfun(@(x) y*sin(2*x) + sin(2*y*x),pi/2:.01:pi,'UniformOutput',false);
plot(y,z{20});%choose whatever x value you want to look at, you could plot several of them using a loop

to find the root, select the interval you are interested in

x=pi/2;
eqn = @(y) y*sin(2*x) + sin(2*y*x);
yRoot = fzero(eqn,[.9 1.1]);% produces root of 1
yRoot = fzero(eqn,[1.9 2.1]);%produces root of 2

Answer 1

[Matt J]

Something like this, perhaps:

x=linspace(pi/2,pi);
for z=(1:100)
    eqn= @(y) sinc(2*x(z)) + sinc(2*y*x(z));
    yRoots(z) = abs(  fzero(eqn,1e-8) )
end