Given a sentence in Tagalog language, translate the sentence to English language keeping the meaning of the original sentence intact.

Q: Tagalog sentence: Sa 1898 Osgood-publish ng isang mahalagang papel sa mga solusyon ng mga kaugalian equation dy / dx = f (x, y) kasiya-siyang ang inireseta unang kondisyon y (a) = b.... Osgood ay nagpakita na kung f (x, y) ay patuloy na may umiiral na lamang ng hindi bababa sa isang solusyon...

A: In 1898 Osgood published an important paper on the solutions of the differential equation dy/dx = f(x, y) satisfying the prescribed initial conditions y(a) = b.... Osgood showed that if f(x, y) is merely continuous there exists at least one solution...
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Q: Tagalog sentence: a) Kung, Patunayan na may mga pagbabagong mula na para sa bawat permutasyon, May index iyon may karaniwang puntos.

A: a) If, prove that there are permutations from that for each permutation, there is an index that have common points.
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Q: Tagalog sentence: 30:27 Sa kanila na nasa Beth-el, at sa kanila na nasa Ramoth ng Timugan, at sa kanila na nasa Jathir;

A:
30:27 To them which were in Bethel, and to them which were in south Ramoth, and to them which were in Jattir,
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