MTH401 ASSIGNMENT 1 SOLUTION SPRING 2021
Total Marks: 10
Due Date: 10-June-2021
Solve the following differential equations:
Question 1:
dydx-2xy=x
, y0=1
SOLUTION:
General Equation
By Comparing Equation (1) and (2)
So, Integrating Factor
Multiply equation (1) by integrating factor
Taking Integration on both sides
Let,
Taking Derivative on both sides
Now equation (3) becomes
Putting initial condition in equation (4)
Putting value of c in equation (4)
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Question 2:
The population of a certain community is known to increase at a rate proportional to the number of people present at any time. The population has doubled in 5 years, how long would it take to triple?
SOLUTION:
Suppose that is the initial population of community and p (t) the population at any time t then the population growth is governed by the differential equation
As we know the solution of a differential equation is given by
Since therefore from the above equation we have
Taking natural log on both sides
Therefore, the solution of the equation becomes
If is t1is the time taken from the population to triple then
Taking natural log on both sides
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MTH401 Assignment 1 Solution 2021
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