Add terms to previously defined differential equation (Symbolic)

I everyone!

I have a question related to the usage of the Symbolic Toolbox to solve differential equations.

Suppose I have already defined the differential equation associated with a mass-spring system:

syms x(t) m k
eq_undamped = m*diff(x,2) + k*x == 0 ;

Now, suppose I want to add the damping term to the left hand of the equation defined above:

syms b
v = diff(x) ;
damping = b*v ;

How can I add damping to the left hand side of eq_undamped, obtaining something like:

eq_damped = m*diff(x,2) + k*x + b*diff(x) == 0 ;

I would like not to enter the equation above manually, but combining the previously defined eq_undamped and damping.

Thanks in advance for your reply!

[VBBV]

eq_damped = m*diff(x,2) + k*x + damping == 0 ;

Answer 1

[madhan ravi]

 eq_damped = lhs(eq_undamped) + damping == rhs(eq_undamped)

[Marco Asperti]

Great! Thank you very much for your help 😊