I need help with 5,6&7 please. #7 is on the other document attached

4 DUE TO FRIDAY OCT 18 AT 10:00AM Problem 7. (20 pts) Consider the following secondorder differential equation: Wt) 6y'(t) + 10W) : test, a Find a particular solution 3; t to the differential equation above. ( ) p (b) Find the general solution to the differential equation above. (0) How many solutions y(t) are there with y(0) = 0 and y'(0) = 1 ? If any, nd them and qualitatively plot their graphs. (d) Let us decide to approximate 65' a 1+ 5t + 1%? +009) via a Taylor expansion and consider the system: 125 t2 . 6 J Find a particular solution 273,6) to this differential equation. t) 6:1:'(t)+ 10m) : t(1 + 515 + (8) Compare the solution yp(t) Obtained in Part (a) with the particular solution $196). Is one related to the Taylor expansion of the other ? Do their long-term behaviors coincide