Solution graph eq37
\[y'' - a\,(y')^2 = f(x)\,e^{ay}\]
All known solutions found
Families found: 1 / 1
Judge: Solutions verified
Solution process: strong
Lean: 8 / 23
All known solutions found. All reference solution families were found (1 of 1). Completeness is not established; this conclusion matches the reference.
How to read the graph
The graph shows how the agent solved the problem, left to right. The answer is in the ★ solution nodes; everything to their left is how it was obtained.
- Problem
- the original equation, the root of the graph.
- Idea N
- a solution plan the agent formulated before trying.
- Variant N
- an attempt along idea N: “✓ gave a solution” or “dead end” (no solution; the whole branch is hidden by the filter).
- ★ Solution N
- the final solution of variant N — a finished answer. “matches reference” — the judge matched it to a solution family of the handbook; “Lean ✓” — its formal part compiles.
- Completeness → Step N
- the argument that there are no other solutions: steps and their solutions; ∎ Completeness conclusion — the result of this branch, if the agent stated one.
- Subtasks, fragments
- (toggle) how a variant was carried out: subtasks and their solutions; green fragments made it into the final solution.
- Judge
- (toggle) LLM-judge nodes: checks of solutions, comparison with the reference, the verdict.
Click a node to see its text, Lean code and check result; “Where it leads” in the panel is the node’s subtree.
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Prompts and raw model outputs are not shown; reference solutions and the judge's retelling of them are hidden.