test: test passing nothing to u0 for all system types

test/discrete_system.jl

@@ -271,3 +271,11 @@ end
 k = ShiftIndex(t)
 @named sys = DiscreteSystem([x ~ x^2 + y^2, y ~ x(k - 1) + y(k - 1)], t)
 @test_throws ["algebraic equations", "not yet supported"] structural_simplify(sys)
+
+@testset "Passing `nothing` to `u0`" begin
+    @variables x(t) = 1
+    k = ShiftIndex()
+    @mtkbuild sys = DiscreteSystem([x(k) ~ x(k - 1) + 1], t)
+    prob = @test_nowarn DiscreteProblem(sys, nothing, (0.0, 1.0))
+    @test_nowarn solve(prob, FunctionMap())
+end

test/nonlinearsystem.jl

@@ -318,3 +318,10 @@ sys = structural_simplify(ns; conservative = true)
     sol = solve(prob, NewtonRaphson())
     @test sol[x] ≈ sol[y] ≈ sol[z] ≈ -3
 end
+
+@testset "Passing `nothing` to `u0`" begin
+    @variables x = 1
+    @mtkbuild sys = NonlinearSystem([0 ~ x^2 - x^3 + 3])
+    prob = @test_nowarn NonlinearProblem(sys, nothing)
+    @test_nowarn solve(prob)
+end

test/odesystem.jl

@@ -1390,7 +1390,7 @@ end
 
 @testset "Passing `nothing` to `u0`" begin
     @variables x(t) = 1
-    @mtkbuild sys = ODEProblem(D(x) ~ t, t)
+    @mtkbuild sys = ODESystem(D(x) ~ t, t)
     prob = @test_nowarn ODEProblem(sys, nothing, (0.0, 1.0))
     @test_nowarn solve(prob)
 end

test/optimizationsystem.jl

@@ -340,3 +340,10 @@ end
     prob.f.cons_h(H3, [1.0, 1.0], [1.0, 100.0])
     @test prob.f.cons_h([1.0, 1.0], [1.0, 100.0]) == H3
 end
+
+@testset "Passing `nothing` to `u0`" begin
+    @variables x = 1.0
+    @mtkbuild sys = OptimizationSystem((x - 3)^2, [x], [])
+    prob = @test_nowarn OptimizationProblem(sys, nothing)
+    @test_nowarn solve(prob, NelderMead())
+end

test/sdesystem.jl

@@ -776,3 +776,11 @@ end
     prob = SDEProblem(de, u0map, (0.0, 100.0), parammap)
     @test solve(prob, SOSRI()).retcode == ReturnCode.Success
 end
+
+@testset "Passing `nothing` to `u0`" begin
+    @variables x(t) = 1
+    @brownian b
+    @mtkbuild sys = System([D(x) ~ x + b], t)
+    prob = @test_nowarn SDEProblem(sys, nothing, (0.0, 1.0))
+    @test_nowarn solve(prob, ImplicitEM())
+end