Regularity of $f\,dt$ at every finite point of $w^2=h(t)$ gives $f\,w=a(t)+b(t)\,w$ with polynomials $a,b$

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Regularity of $f\,dt$ at every finite point of $w^2=h(t)$ gives $f\,w=a(t)+b(t)\,w$ with polynomials $a,b$ · Prove2Me