For each of the following differential equations, state the order and determine whether it is linear or nonlinear. If the differential equation is linear, state whether it is homogeneous or nonhomogeneous

a. (1 − x)y'' − 3xy' + 7y = cos x
b. x 4y x 4 − 3 ( y x) 5 − y x − 6y = 0
c. y ′′′ − x 2y ′′ + y = tan y

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241. a) 0 b) 1 c) 2 d) 1 2

Which is a true statement comparing the graphs of x^2/6^2-y^2/8^2 = 1 and x^2/8^2-y^2/6^2 the foci of both graphs are the same points. the lengths of both transverse axes are the same. the directrices of = 1 are horizontal while the directrices of = 1 are vertical. the vertices of = 1 are on the y-axis while the vertices of = 1 are on the x-axis.

Two cars which are 40 miles apart start moving simultaneously in the same direction with constant speeds. if the speed of the car which is behind is 56 mph and the speed of the other car is 48 mph, how many hours will it take for the car which is behind to catch up the car ahead of it?