# How to solve a simple symbolic identity?

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DH on 30 May 2023
Answered: DH on 30 May 2023
I have the following identity.
The solution is .
I wrote the following code.
syms w0 a b t m F0;
eqn = 2*b*w0*cos(w0*t) - 2*a*w0*sin(w0*t) == (F0*cos(w0*t))/m;
sol = solve(eqn, [a b])
sol = struct with fields:
a: -(F0*cos(t*w0))/(2*m*w0*sin(t*w0)) b: 0
The sol is not what I want to get.
Could you tell me how to get the correct a and b, i.e., ?
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### Accepted Answer

DH on 30 May 2023
Thank you VBBV.
Based on your reply, I wrote the following code:
syms w0 a b t m F0;
eqn = 2*b*w0*cos(w0*t) - 2*a*w0*sin(w0*t) == (F0*cos(w0*t))/m;
eq1 = subs(eqn, t, 0.5);
eq2 = subs(eqn, t, 0.6);
sys_eqn = [eq1 eq2];
sol = solve(sys_eqn, [a b])
sol = struct with fields:
a: 0 b: F0/(2*m*w0)
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### More Answers (1)

VBBV on 30 May 2023
syms w0 a b t m F0
eqn = 2*b*w0*cos(w0*t) - 2*a*w0*sin(w0*t) == (F0*cos(w0*t))/m;
sol = solve(eqn, [b])
sol =
b = subs(sol,t,0)
b =
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VBBV on 30 May 2023
Edited: VBBV on 30 May 2023
Solve for b variable and substitute t as zero, since you have only one equation, you can solve for only one variable. The solution to a doesnt exist for t = 0.

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