test: test that singular initialization systems throw a warning

test/initializationsystem.jl

@@ -947,3 +947,14 @@ end
 
     @test_nowarn remake(prob, p = prob.p)
 end
+
+@testset "Singular initialization prints a warning" begin
+    @parameters g
+    @variables x(t) y(t) [state_priority = 10] λ(t)
+    eqs = [D(D(x)) ~ λ * x
+           D(D(y)) ~ λ * y - g
+           x^2 + y^2 ~ 1]
+    @mtkbuild pend = ODESystem(eqs, t)
+    @test_warn ["structurally singular", "initialization", "guess"] ODEProblem(
+        pend, [x => 1, y => 0], (0.0, 1.5), [g => 1], guesses = [λ => 1])
+end