# Question 1958: Highest Explicit Derivative Order, Not Candidate Polynomial Degree [Return to catalogue page 10](https://ocme.evemisslab.com/en/questions/page/10/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations/#q-20261013-advance-20261020-r02-ordinary-differential-equation-0008) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0002-01958 · q-20261013-advance-20261020-r02-ordinary-differential-equation-0008 ## Original question and givens Derivative orders occurring in the specified relation are [3], with 0 denoting y itself. Give (sorted distinct orders, highest order, does y occur?). A [0]-only list records the algebraic order-zero boundary, not evidence of a positive-order ODE. - G001 — Derivative orders occurring in the specified relation are [3], with 0 denoting y itself. Give (sorted distinct orders, highest order, does y occur?). A [0]-only list records the algebraic order-zero boundary, not evidence of a positive-order ODE. ## Definition and scope Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate. - [mko-ordinary-differential-equation](https://ocme.evemisslab.com/en/mko/mko-ordinary-differential-equation/) ## Step-by-step derivation S001 · impliesBefore [3] After distinct actual derivative orders=[3] Conditions: none Classify using the explicitly present derivative orders;sorting and deduplication add no derivative terms. Step identifiers and dependenciesRule: derivative_order_list · Uses: G001 S002 · impliesBefore [3] After highest listed order=3 Conditions: none Take the highest order,not the number of entries in the list. Step identifiers and dependenciesRule: highest_derivative_order · Uses: G001, S001 S003 · impliesBefore 0 in orders: No After order0 denotes the undifferentiated y term Conditions: none The third flag asks whether y itself occurs;its presence does not make the whole equation order0. Step identifiers and dependenciesRule: includes_y_flag · Uses: G001, S002 S004 · impliesBefore highest=3; includes_y=No After classification assumes the listed terms survive simplification Conditions: none A list containing only0 is the algebraic boundary;this classification proves no existence,uniqueness or candidate-solution claim. Step identifiers and dependenciesRule: order_not_existence_theorem · Uses: G001, S003 ## Reverse checks - S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. ## Result ([3], 3, No) The full substitutions and premise checks give the original answer; source identity,format and status are unchanged. ## This question review and source binding Review date: 2026-10-26 Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: ac27e6a432eef2d015b06084231c6f35b5a9508f814c4a004cbdf8ada0042a7d - candidate record SHA-256: a19ff201e1aba9b4c8f944768cc582f1db648f80a57d0edc003d23959a4f4d73 - semantic review receipt SHA-256: 340d74dcc6e37df6249594a0b79a9ee2af804337b7847478b3c1342af9722861 - question-first witness SHA-256: 9a06233d190d31a16f13fb03b6c3ceba4cbb748fff6c997941f66ab1888dcca8 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261013-advance-20261020-r02-ordinary-differential-equation-0008.json)