Differential Equations Answers

3d^2y/dx^2+dy/dx-14y=0 ; y(0)=1 , y'(0)=-1

show that y=c1e^x+c2e^2x is the general solution of y′′−3y′+2y=0 on any interval and find the particular solution for which y(0)=-1 and y'(0)=1

(y - xy)dx + xdy = 0

A research is being done on a particular species of bear on an animal reserve territory. Initially, there are 50 bears on the reserve. After t years the number of bears, n, satisfies the differential equation "dn" / "dt" = 1 / "20k" n(k-n), where k are constant.

a.) By using saperable viarable, show that the general solution of the differential equation is n = 200 / 1 +3e^-0.05t given that k = 200 [14 marks]

b.) In 2012, the population of the bears in the territory are 200. Estimate the population of the bears that will be able to survive after 2022. [3 marks]

The differential equation which has y 4 = Cx3 − 3 as its general solution is:

Solve (d ^ 2 * y)/(d * x ^ 2) - 2tan x * (dy)/(dx) + 5y =

Find the general solution to the differential equation 4d^2y/dx^2+4dy/dx+y=0

A thermometer is taken from a room where the temperature is 20°C to the outdoors,

where the temperature is 5°C. After one minute the thermometer read 12°C.Use

Newton’s Law of Cooling to answer the following questions:

a) What will the reading on the thermometer be after one more minute?

b) When will the thermometer read 6°C?

Find a power series solution of xy'=y