How to plot multiple curves in a single figure by varying a parameter?

I have the following equation :-

my x ranges from (-5,10).

I want to plot multiple curves (y vs x) of the following equation by varying the parameter 'c' i.e giving some discrete values of 'c'.

How do I do that using a for loop?

Answer 1

[Star Strider]

No loop required.

Try this —

syms c x y 
Eqn = y^2/2-cos(x) == c

Eqn = 

y = solve(Eqn,y)

y = 

yfcn = matlabFunction(y, 'Vars',{x,c})

yfcn = function_handle with value:
    @(x,c)[sqrt(2.0).*sqrt(c+cos(x));-sqrt(2.0).*sqrt(c+cos(x))]

xv = linspace(-5, 10, 25);
cv = 0:5;
[X,C] = ndgrid(xv,cv);

ymtx = yfcn(X,C);
% Q1s = size(ymtx)

figure
surf(X,C,real(ymtx((1:numel(xv)),:)))
hold on
% surf(X,C,imag(ymtx((1:numel(xv)),:)))
surf(X,C,real(ymtx((1:numel(xv))+numel(xv),:)))
% surf(X,C,imag(ymtx((1:numel(xv))+numel(xv),:)))
hold off
grid on
xlabel('x')
ylabel('c')
zlabel('y(x,c)')

figure
plot(xv, real(ymtx((1:numel(xv)),:)))
hold on
plot(xv,real(ymtx((1:numel(xv))+numel(xv),:)))
hold off
grid on
xlabel('x')
ylabel('y')
legend(compose('c = %d',cv), 'Location','bestoutside')

figure
fsurf(y, [-5 10  1 5])
xlabel('x')
ylabel('c')
zlabel('y(x,c)')

Make appropriate changes to get the result you want.

EDIT — 13 Aug 2021 at 15:42)

Corrected typographical error in the second figure plot calls (originally plotted against wrong variable).

.

Answer 2

[Matt J]

for c=1:5

    fimplicit( @(x,y) y.^2/2-cos(x) - c)
    hold on
    
end
hold off
xlim([-5,10])