Question

Question 1 (6 marks) Solve the initial-value problem frac{dy}{dx} = frac{1}{x^3y}, y(1) = 2 where x > 0 and y > 0. Question 2 (6 marks) Find the particular integral of the following differential equation ddot{x} - 5dot{x} + 6x = 4e^{-2t}. Question 3 (6 marks) Use Gaussian elimination to solve the system of linear equations, in three unknowns x_1, x_2 and x_3, given in augmented matrix form by egin{bmatrix} 0 & 1 & 2 & | & -2 \ 1 & -2 & 3 & | & -9 \ 2 & -4 & 3 & | & -12 end{bmatrix}.

          Question 1 (6 marks)
Solve the initial-value problem
frac{dy}{dx} = frac{1}{x^3y}, y(1) = 2
where x > 0 and y > 0.

Question 2 (6 marks)
Find the particular integral of the following differential equation
ddot{x} - 5dot{x} + 6x = 4e^{-2t}.

Question 3 (6 marks)
Use Gaussian elimination to solve the system of linear equations, in three unknowns x_1, x_2 and x_3, given in augmented matrix form by
egin{bmatrix} 0 & 1 & 2 & | & -2 \ 1 & -2 & 3 & | & -9 \ 2 & -4 & 3 & | & -12 end{bmatrix}.

Show more…

$Question 1 (6 marks) Solve the initial-value problem fracdydx = frac1x^3y, y(1) = 2 where x > 0 and y > 0. Question 2 (6 marks) Find the particular integral of the following differential equation ddotx - 5dotx + 6x = 4e^-2t. Question 3 (6 marks) Use Gaussian elimination to solve the system of linear equations, in three unknowns x1, x2 and x3, given in augmented matrix form by eginbmatrix 0 1 2 | -2 1 -2 3 | -9 2 -4 3 | -12 endbmatrix.$

Added by Stacy B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/14/2023

Step 1

To solve this, we need to find the general solution of the differential equation and then use the initial condition to find the particular solution. The differential equation is not given, so we cannot solve it. Show more…

Show all steps

lock

Thanks for your feedback!

Question 1 (6 marks) Solve the initial-value problem y(1) = 2 where x > 0 and y > 0. Question 2 (6 marks) Find the particular integral of the following differential equation Question 3 (6 marks) Use Gaussian elimination to solve the system of linear equations, in three unknowns x1, x2, and x3, given in augmented matrix form by

Play audio

Feedback

Powered by NumerAI

Adi S and 80 other subject Calculus 3 educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:03 In this question we are given a differential equation dy by dx is equal to 1 upon x cube y where the initial value condition is y of 1 is equal to 2.

00:17 Now we can solve this equation by using the method of separation of variables.

00:28 So now we will separate the variable of x and the variables of y.

00:34 We can see that here it is dy and after doing the cross product we are getting x cube y into dy is equal to dx.

00:45 Now we will be getting y into dy is equal to dx upon take this x cube to the right hand side and it will be in denominator.

00:55 So now after integrating on both sides, integrating both sides we will be getting y into dy will be y square by 2 is equal to integration of x to the power 3 with respect to this.

01:14 So this is basically integration of x to the power minus 3.

01:17 So x to the power minus 3 plus 1 upon minus 3 plus 1 plus constant of integration.

01:24 So that will be equal to y square by 2 is equal to x to the power minus 2 upon minus 2 plus c.

01:34 Similarly we can write it as y square by 2 is equal to minus 1 by 2 upon x to the power 2 plus c.

01:45 Alright.

01:46 Now we have to put our initial value condition that is given by y of 1 is equal to 2.

01:53 Okay now we will use it.

01:54 So the value of y is given to be 2.

01:57 So 2 square upon 2 this is equal to minus 1 upon 2 into 1 square which is 1 plus...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later