How to solve two simultaneous equations using solve command?

I want to solve these two simultaneous equations:

eqn1 = 0.75*k*B1^3 + 0.75*k*B1*B2^2 - m*w^2*B1 + c*B1 -D*w*B2- A == 0

eqn2 = 0.75*k*B2^3 + 0.75*k*B2*B1^2 - m*w^2*B2 + c*B2 -D*w*B1 == 0

and find what is the (B1^2+B2^2)^(1/2) (square root of B1 squared plus B2 squared ) and also plot the (B1^2+B2^2)^(1/2) Vs w.

So far I wrote my code until here and i dont know how to continue:

syms A m c k w D B1 B2

eqn1 = 0.75*k*B1^3 + 0.75*k*B1*B2^2 - m*w^2*B1 + c*B1 -D*w*B2- A == 0;

eqn2 = 0.75*k*B2^3 + 0.75*k*B2*B1^2 - m*w^2*B2 + c*B2 -D*w*B1 == 0 ;

eqn1 = subs(eqn1, [k,m,c,A,D], [0.2,1,1,1,0.2]);

eqn2 = subs(eqn2, [k,m,c,A,D], [0.2,1,1,1,0.2]);

sol1 = abs(solve(eqn1,B1));

sol2 = abs(solve(eqn2,B2));

Answer 1

[Walter Roberson]

[B1sol, B2sol] = solve([eqn1,eqn2],[B1,B2]);
Y = sqrt(B1sol.^2 + B2sol.^2);

fplot(Y)

These involve fifth order polynomials, so there are 5 solutions, and plotting is rather slow.

Unfortunately, the root() operation that is generated symbolically cannot be translated using matlabFunction, so this cannot easily be translated into a numeric function.

[Walter Roberson]

 W = linspace(-5,5);
 nY = double(subs(Y.',w,W.'));
 nY(imag(nY)~=0) = nan;
 plot(W, nY)

[Jen Cong Wong]

Thank you so much. But is it possible to plot from 0 to 5? I changed the linspace value from 0 to 5 and matlab said:

Error using symengine
Division by zero.

Error in sym/subs>mupadsubs (line 140)
G = mupadmex('symobj::fullsubs',F.s,X2,Y2);

Error in sym/subs (line 125)
G = mupadsubs(F,X,Y);

Error in NonlinearStudyWithDamping (line 19)
nY = double(subs(Y.',w,W.'));

[Walter Roberson]

w = 0 is a special case . You need to either ignore it by starting to plot from something greater than 0, or you need to handle it before you do the solve()

For the ignore-it route:

W = linspace(realmin,5);
nY = double(subs(Y.',w,W.'));
nY(imag(nY)~=0) = nan;
plot(W, nY)

Otherwise:

[B1sol0, B2sol0] = solve(subs([eqn1,eqn2], w, 0), [B1,B2]);
nY0 = double( sqrt(B1sol0.^2 + B2sol0.^2) );
nY0(imag(nY0)~=0) = nan;
plot(0, nY0, '*');
hold on

and then do the above "ignore-it" code.

There is only a single real root at w = 0

[Jen Cong Wong]

This works! Thank Walter!