Yassin ElBedwihy

Issue #961, solve_for outputting wrong answers when function is nonlinear.

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The `linear_expansion()` function sees `x*y ~ 0` as linear due to looping over the lhs variable by variable, while observing the other variables as a constant. For example, when observing...

isaffine and islinear not handling differentials correctly

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```julia @variables x y t D = Differential(t) Dx = D(x) expr = Dx * x + Dx*t - 2//3*x + y*Dx Symbolics.isaffine(expr - Dx, [x]) # ERROR: Failed to...

changed output format of zero dimension sols

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Now, alex's latest issue #1235 's output is returned as ```julia julia> symbolic_solve([(x - y) * (x - z) * (y - z)], [x,y,z]) 2-element Vector{Dict{Num, Any}}: Dict(x => y)...

x+im = 0 is linear?

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```julia julia> @variables x 1-element Vector{Num}: x julia> Symbolics.solve_for(x+im, x) ERROR: AssertionError: islinear ```

WIP: BVP Out of Place Linear problems

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## Checklist - [ ] Appropriate tests were added - [ ] Any code changes were done in a way that does not break public API - [ ] All...

From [this discourse post](https://discourse.julialang.org/t/solve-can-not-solve-nonlinear-symbolic-equations/122942/3): ```julia @variables e_x[1:3] heading = 0.01 eqs = [ atan(-e_x[2]/-e_x[1]) ~ heading norm(e_x) ~ 1.0 e_x[2] ~ 1.0 ] ``` ```julia Equations: Equation[atan(e_x[2] / e_x[1]) ~...

```julia julia> symbolic_solve(-2+b+1/b, b) ┌ Warning: This expression cannot be solved with the methods available to ia_solve. Try a numerical method instead. └ @ Symbolics ~/code/julia/Symbolics.jl/src/solver/ia_main.jl:27 ```

Groebner basis failing with time-dependent variables

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```julia @variables t S(t) R(t) Symbolics.groebner_basis(expr) Symbolics.groebner_basis(expr, ordering=Lex(S, R)) ``` Output: ```julia julia> Symbolics.groebner_basis(expr) 2-element Vector{PolyForm{Real}}: -12 + 5S(t) 2 + 5R(t) julia> Symbolics.groebner_basis(expr, ordering=Lex(S, R)) ERROR: DomainError with Lex{Num}(Num[S(t),...