Differential Equations Answers

There are 10000 people living in a certain city. Suppose that the rate of population growth in the city is proportional to the number of inhabitants. Suppose that 20% of the original amount increase in 20 years, how much will the population in the city after 40 years?

Initially, there are 1 million bacteria present in a Petri dish. After 2 minutes, there are already 5 million of them. If the bacterial population follows a law of natural growth, how many bacteria should be present in the Petri dish after 5 minutes?

Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5 million pesos. After 2 years, the value decreased to 1.2 million pesos. If the amount of the car is directly proportional to the constant rate of decay in amount and such decrease in amount continues at the same rate, then how much is the estimated value of the car after 10 years?

(D^3+2D^2D'-DD'^2-2D'^3)z=(y+2)e^x

y'' - 3y' - 10y = 0 ; y(0)=1 and y'(0)=10

dy/dx-y= e^x y^2

X^2 - y^2 = cx

Solve the following differential equations : (x + cosy)dx + (-xsiny)=0