Question

2. [2] If the velocity at time t for a particle moving along a straight line is proportional to the square root of its position x, write a differential equation that fits this description 3. [4] Show that y(x) = e* - x is an explicit solution to the differential equation dy y2 e2x e* - 2xe* + x2 - 1 on the entire real line = dx

Answer 1

2 2. dz dt Here, where Y& i it position ; k i troporkionality Censtam dx dt 3. s explicihsolution f If y(x)= e x than dy dn 2X satis fy e-x duy e 1 dx day da Nos, L.HS (e e+

2X 2х е* + х* 11 - R.HS e?* +еx- 2хе*+ ~1. 11 I У a) - е^- х js eapliit soluiom of