Confusing behavior while defining list of equations for a multi vaiable system

[soumyasrtk]

For a set of equations,

# define equation of motion
@variables ω1, ω2, t, ω, F, γ, α1, α2, k, x(t), y(t);
eqs = [ d(x, t, 2) + ω1^2 * x + γ*d(x,t) + α1*x^3 - k*y, 
                    d(d(y,t),t) + ω2^2*y + γ*d(y,t) + α2*y^3 - k*x]

diff_eq = DifferentialEquation(eqs~[F*cos(ω*t), 0], [x, y])

System of 1 differential equations
Variables:       x(t)
Harmonic ansatz: x(t) => ;   

Symbolics.Num[Differential(t)(Differential(t)(x(t))) - k*y(t) + Differential(t)(x(t))*γ + x(t)*(ω1^2) + (x(t)^3)*α1, Differential(t)(Differential(t)(y(t))) - k*x(t) + Differential(t)(y(t))*γ + y(t)*(ω2^2) + (y(t)^3)*α2] ~ Symbolics.Num[F*cos(t*ω), 0]

gives a different result than

# define equation of motion
@variables ω1, ω2, t, ω, F, γ, α1, α2, k, x(t), y(t);
eqs = [ d(x, t, 2) + ω1^2 * x + γ*d(x,t) + α1*x^3 - k*y, 
                    d(d(y,t),t) + ω2^2*y + γ*d(y,t) + α2*y^3 - k*x]-[F*cos(ω*t), 0]

diff_eq = DifferentialEquation(eqs, [x, y])

System of 2 differential equations
Variables:       x(t), y(t)
Harmonic ansatz: x(t) => ;   y(t) => ;   

Differential(t)(Differential(t)(x(t))) - F*cos(t*ω) - k*y(t) + Differential(t)(x(t))*γ + x(t)*(ω1^2) + (x(t)^3)*α1 ~ 0
Differential(t)(Differential(t)(y(t))) - k*x(t) + Differential(t)(y(t))*γ + y(t)*(ω2^2) + (y(t)^3)*α2 ~ 0

[oameye]

Thanks for the report :)

You are using wrong syntax in the first example. eqs is a vector of Num (symbolic expression). Writing eqs~[F*cos(ω*t), 0] equates the vectors so that the type would be Symbolics.Num[...] ~ Symbolics.Num[...]. However, you would to equate the indivual expressions. Broadcasting the equation symbol ~ gives Vector{Equation}, i.e., eqs .~ [F*cos(ω*t), 0] (Notice, .~ vs ~.)

@variables ω1, ω2, t, ω, F, γ, α1, α2, k, x(t), y(t);
rhs = [ d(x, t, 2) + ω1^2 * x + γ*d(x,t) + α1*x^3 - k*y,
        d(d(y,t),t) + ω2^2*y + γ*d(y,t) + α2*y^3 - k*x]
eqs = rhs.~[F*cos(ω*t), 0]

diff_eq = DifferentialEquation(rhs .~[F*cos(ω*t), 0], [x, y])

Nevertheless, we should throw an argument error. Will implement this.