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

SOLUTION: 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...

PROBLEM: Tagalog sentence: Ang kanyang mga pag-uusap ay isang usisero timpla ng hangin at kagaslawan.

SOLUTION: His conversation was a curious mixture of pomposity and wantonness.

PROBLEM: Tagalog sentence: Siya ay nagsimulang isang malubhang pag-aaral ng German at yari siya sa kasaysayan at panitikan na kung saan ay siya ang sikat.

SOLUTION:
He began a serious study of German and he turned to history and literature for which he is famed.