# Solve NonlinearProblem

There some NonlinearProblem example.

## NLP examples

solve function:

$$$\left\{\begin{matrix} x^2 + y^2 + z^2 = 1.0\\2 x^2 + y^2 - 4 z = 0 \\ 3 x^2 - 4 y^2 + z^2 = 0\end{matrix}\right.$$$

julia code:

@variables x, y, z
eqs = [
x^2 + y^2 + z^2 ~ 1.0
2 * x^2 + y^2 - 4 * z ~ 0
3 * x^2 - 4 * y^2 + z^2 ~ 0
]
vars = Dict(x => 2.0, y => 1.0, z => 1.0)
pro = NLProblem(eqs, vars)
res = solve(pro)
@show res

res = Dict{Num, Float64}(
y => 0.6285242979602138,
z => 0.3425641896895694,
x => 0.6982886099715139
)

solve function:

$$$\left\{\begin{matrix}cos(x^2 + 0.4 y) + x^2 + y^2 = 1.6\\1.5 x^2 - 1 / 0.36 * y^2 = 1.0\end{matrix}\right.$$$

julia code:

@variables x, y
eqs = [
cos(x^2 + 0.4 * y) + x^2 + y^2 ~ 1.6
1.5 * x^2 - 1 / 0.36 * y^2 ~ 1.0
]
vars = Dict(x => 2.0, y => 1.0)
pro = NLProblem(eqs, vars)
res = solve(pro)

res = Dict{Num, Float64}(
y => 0.47172595266055173,
x => 1.0386292376770578
)

solve function:

$$$\left\{\begin{matrix}4 x + 0.1 * e^x = y + 1\\4 y + x^2 / 8 = x\end{matrix}\right.$$$

julia code:

@variables x, y
eqs = [
4 * x + 0.1 * exp(x) ~ y + 1
4 * y + x^2 / 8 ~ x
]
vars = Dict(x => 2.0, y => 1.0)
pro = NLProblem(eqs, vars)
res = solve(pro)

res = Dict{Num, Float64}(
y => 0.056451519652141575,
x => 0.23256700509067185
)