# Add terms to previously defined differential equation (Symbolic)

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Marco Asperti on 10 Oct 2020
Commented: Marco Asperti on 10 Oct 2020
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.
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VBBV on 10 Oct 2020
Edited: VBBV on 10 Oct 2020
eq_damped = m*diff(x,2) + k*x + damping == 0 ;

madhan ravi on 10 Oct 2020
eq_damped = lhs(eq_undamped) + damping == rhs(eq_undamped)
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Marco Asperti on 10 Oct 2020
Great! Thank you very much for your help 😊

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