The word पत्या (Patyā) in the third case (तृतीया - Instrumental) is actually grammatically correct here due to the rules of causal verbs (णिजन्त - Causative) in Sanskrit.
Using पत्युः (Patyuḥ) in the sixth case (षष्ठी - Genitive) would be grammatically incorrect in this specific sentence structure.
Here is the exact grammatical breakdown of why this happens.
1. The Rule of the Causative Agent (प्रयोज्य कर्ता)
In a normal sentence, the person doing the action is the subject (कर्ता) and takes the 1st case (प्रथमा).
- Normal: पतिः स्नानं करोति। (The husband does the bath / takes a bath.)
When you change the verb into a causative/prompted action (कारयति - causes to do / makes someone do), the original subject becomes the "prompted agent" (प्रयोज्य कर्ता).
According to Panini's grammar rule (कर्तृकरणयोस्तृतीया - 2.3.18), the prompted agent of a causative verb generally takes the तृतीया विभक्ति (Third Case), unless it falls under specific exceptions (like verbs of motion, eating, or knowing).
Since कृ (to do/make) does not fall under those exceptions:
- The husband (the one being made to bathe) must be in the तृतीया विभक्ति.
- Causative: (सा) पत्या स्नानं कारयति। ([She] makes the husband take a bath / causes bathing by the husband.)
2. Why Genitive (पत्युः) is Incorrect
If you change it to the Genitive case (पत्युः), the sentence would mean: "She causes the bath of the husband [by someone else]."
While Genitive can show possession, Panini's syntax requires the actual doer of the action (even in a causative sentence) to be expressed in either the 2nd (द्वितीया) or 3rd (तृतीया) case depending on the verb root. For the root कृ (कारयति), the 3rd case is the standard rule.
3. A Brief Word Form Check
Just to clarify the declension (शब्दरूप) of the cargo word पति (Husband):
- पत्या = तृतीया विभक्ति, एकवचन (Instrumental Singular) — "by/through the husband"
- पत्युः = पञ्चमी / षष्ठी विभक्ति, एकवचन (Ablative/Genitive Singular) — "from/of the husband"
Therefore, पत्या is the precise and correct grammatical choice for this sentence.