Is Solving 0.2y - 0.02x - 0.5 = 0 Correct for Finding a Straight Line Equation?

[Natasha1]

I'm given the differential equation dy/dx = 0.2y - 0.02x and I am asked to obtain a straight line equation for dy/dx = 0.5

Does this mean need to solve the quadratic 0.2y - 0.02x - 0.5 = 0 ?

 

[Hootenanny]

I hate to burst your bubble but

0.2y - 0.02x - 0.5 = 0

Isn't a quadratic. Is the question phrased exactly as you have typed?

~H

 

[Natasha1]

Well the whole exercise is as follows:

The spread of a disease in a community is modeled by the following differential equation:

dy/dx = 0.2y - 0.02x where y is the number of infected individuals in thousands, and x the time in days.

1) Show the equation that for the family of 'curves' in the plane for which dy/dx is a constant, is the form y=mx+c.

2) Obtain the four straight line equations for dy/dx equal to 0.5, 1, 2 and 3

3) Solve the equation using the linear 1st order method, given that initially there are on thousand infected individuals.

Help please :-)

 

[Hootenanny]

Ok, for question two, it is basically asking you to find the equation of a straight line for when the rate of infection is 500 infections per day. So what you did above; 0.2y - 0.02x - 0.5 = 0 is correct. Simply re-arrange this into the form y = mx +c.

~H