**MTH401 Assignment 1 Solution 2021.**View Solved Assignment Solution Step by Step Method.

**Download MTH401 Assignment 1 Solution**Spring 2021 below.

MTH401 ASSIGNMENT 1 SOLUTION SPRING 2021

**Solution Perform in MathType Software**

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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