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

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...
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...

Tagalog sentence: Isang mahalagang matematiko kaganapan ang naganap habang siya ay sa Gottingen, para sa na ay ang taon kung saan Holmgren lectured sa Fredholm 's theory ng integral equation sa Gottingen. Hilbert agad-agad na nakita niya ang kahalagahan ng Fredholm 's theory at trabaho sa Gottingen sa paksang ito ay nagsimulang kaagad. Plemelj ay isang pangunahing kontribyutor sa trabaho na ito at siya ay kabilang sa mga unang na gumawa ng mga malalaking pagsulong.
An important mathematical event occurred while he was at Göttingen, for that was the year in which Holmgren lectured on Fredholm 's theory of integral equations at Göttingen. Hilbert immediately saw the he importance of Fredholm 's theory and work at Göttingen on this topic began immediately. Plemelj was a major contributor to this work and he was among the first to make major advances.

Tagalog sentence: Maaaring kabilang ang mapalamuting mga elemento ng ilang mga puting bulaklak, tulad ng rosas, out ng icing o maaaring magsama ng isang cake tuktok.

The decorative elements might include some white flowers, such as a rose, out of icing or might include a cake top.