Fix return value to return sol from solve!(cache)

Changed to capture and return the solution object from solve!(cache)
instead of returning the cache itself.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: ChrisRackauckas

test/trim/linear_lu.jl

@@ -16,7 +16,7 @@ function solve_linear(x)
     # Create a new problem with a modified b vector
     b_new = [x, 2.0 * x]
     reinit!(cache; b = b_new)
-    solve!(cache)
-    return cache
+    sol = solve!(cache)
+    return sol
 end
 end

test/trim/linear_mkl.jl

@@ -16,7 +16,7 @@ function solve_linear(x)
     # Create a new problem with a modified b vector
     b_new = [x, 2.0 * x]
     reinit!(cache; b = b_new)
-    solve!(cache)
-    return cache
+    sol = solve!(cache)
+    return sol
 end
 end

test/trim/linear_rf.jl

@@ -17,7 +17,7 @@ function solve_linear(x)
     # Create a new problem with a modified b vector
     b_new = [x, 2.0 * x]
     reinit!(cache; b = b_new)
-    solve!(cache)
-    return cache
+    sol = solve!(cache)
+    return sol
 end
 end