Simple Separable Differential Equation

Click For Summary

Homework Help Overview

The discussion revolves around solving a separable differential equation of the form y' = y^2sinx. Participants are exploring the integration techniques and transformations involved in the problem.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the separation of variables and the integration process, with one suggesting a substitution involving u = y^2. There are questions about the correctness of the integration steps and the resulting terms.

Discussion Status

The discussion includes attempts to clarify the integration steps and the implications of the substitution. Some participants express uncertainty about the results and the need for proper integration of specific terms.

Contextual Notes

There are indications of confusion regarding the integration of 1/y^2 and the overall setup of the problem. Participants are navigating through the assumptions made in the transformation and integration process.

BarackObama
Messages
13
Reaction score
0

Homework Statement


y' = y^2sinx


Homework Equations





The Attempt at a Solution


dy/dx = y^2sinx
dy/y^2 = dxsinx
integral(dy/y^2) = integral(sinxdx)

Aside:
let u = y^2
du = 2ydy
dy = du/2y

ln(abs(y^2))/2y = -cosx+C

integral(du/2y^3) = integral(sinxdx)
 
Physics news on Phys.org
Good morning, Mr President! :smile:
BarackObama said:
Aside:
let u = y^2
du = 2ydy
dy = du/2y

ln(abs(y^2))/2y = -cosx+C

integral(du/2y^3) = integral(sinxdx)

hmm … you're not going to get a second term like that. :redface:

You need the integral of 1/y2

surely you know what that is anyway?? :smile:
 
Thanks!

y= 1/(cosx + C)
 
Yup! :biggrin:
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
3
Views
2K
Replies
3
Views
2K