Solution of non linear equation

Hello,

Let tan(y)-c*tan(a*y)=0 be an equation.

question; is there any a and c such that this equation dos not have any solution. when i apply this code i obtain the empty set:

syms y c a

eq1 = tan(y)-c*tan(a*y);

gargar = solve(eq1)

then gargar = empty set. I think that this mean that there exists a and c such that our equation does not have any solution. But i cannot find this two reals a and c. please help.

[Bjorn Gustavsson]

I think you go about this problem wrongly. Make plots for a few combinations of a and c and see what the curves (both tan(x) and c*tan(a*x)) look like, over a range of -4.7*pi <= x <= 5.17*pi. Then you'll get a better grasp of what's going on.

HTH

[Abdessami Jalled]

Thak you for the advice. please I tried to do this but connot find a code. sorry i'm new in Matlab.

[Bjorn Gustavsson]

Here's some sample code:

x = linspace(-4.7*pi,4.17*pi,3013); % Generate an array for the independent variable
a = 0.2; % some values for a 
c = 5;   % and c
plot(x,tan(x))
hold on
plot(x,c*tan(a*x))
axis([-15 15 -22.5 22.5])

The thing is that you should then think about what the curves imply - you have two piece-wise continuous functions, what has to be true for them never to be equal? This part is not a question

for computations - numerical or sybolic - but for thinking.

[Abdessami Jalled]

thanks to you. what i want is that the to curves does not intersect in 0. and i think this is what i can see

Answer 1

[darova]

Maybe there is no such a and c! I used isosurface to create several combinations:

clc,clear
cla

[a,c,y] = meshgrid(0:0.5:5);
f = tan(y)-c.*tan(a.*y);
p = patch( isosurface(a,c,y,f,0) ); % create surface when f=0

set(p,'FaceColor','red','EdgeColor','none');
daspect([1,1,1])
view(3); axis tight
camlight 
lighting gouraud

xlabel('a axis')
ylabel('c axis')
zlabel('y axis')

This is what i got

And projection XY projection. As you can see there is no such a and c on [0 .. 5] such that f ~= 0

[darova]

looks like something smart for [ 0 : 0.1 : 5 ]