Differential Equations Answers

2.2. Solve the ivp sin(x) dx + y dy = 0, where y(0)

2.1. Solve 2xy + 6x + (x^2 - 4)y'=0

Find the general solution of the given differential equation.

y' + 3x²y = x²

xdy/dx = x² +5y

dx dt=2x-4y 

dx dt=2x+4y

x^2dy/dx-3y^4=2xy

Undetermined Coefficients

4. y^ prime prime +2y^ prime +5y=1+e^ x

27y-8(dy/DX)³=0

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?