Are there multiple valid solutions for the given initial value problem?

  • Context: Undergrad 
  • Thread starter Thread starter footballxpaul
  • Start date Start date
  • Tags Tags
    Diff eq
Click For Summary

Discussion Overview

The discussion revolves around solving a specific initial value problem (IVP) represented by the differential equation (2x-y)dx+(2y-x)dy=0 with the initial condition y(1)=3. Participants explore the validity of their solutions and compare them to a provided answer in a textbook.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The original poster (OP) claims to have solved the IVP and arrived at the equation 2y+2x=C, leading to 2y+2x=8, but questions the correctness of their solution compared to the textbook answer.
  • Some participants ask for clarification on the initial condition y(1)=3 and the method used to arrive at the OP's solution.
  • One participant suggests that the problem is straightforward and encourages the OP to show their work, indicating that the equation is exact and can be integrated easily.
  • Another participant asserts that the OP's solution is incorrect and provides reasoning based on the differential equation's structure.
  • There is a claim that both the OP's solution and the textbook solution appear to be extraneous, indicating potential issues with both approaches.

Areas of Agreement / Disagreement

Participants express disagreement regarding the correctness of the solutions presented. There is no consensus on which solution is valid, and multiple competing views remain regarding the interpretation of the problem and the methods used.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in solving the IVP, and there are indications of missing assumptions or dependencies on specific methods of integration.

footballxpaul
Messages
30
Reaction score
0
(2x-y)dx+(2y-x)dy=0 y(1)=3

solve the given initial value problem and determine at least approx where the solution is valid?


this should be simple right? I got 2y+2x=C and then 2y+2x=8. It doesn't match the answer in the back of the book at all, and I do see how they could have gotten the answer in the back. Is my answer right? The book says y=[x+sqrt(28-3x^2)]/2, abs(x)<sqrt(28/3)? or is the book right, and if so how do you get to their answer?
 
Last edited:
Physics news on Phys.org
How did you get your answer, and what's that y(1) on the end?
 
its y(1)=3, I just solve the ivp by using the exact method. It seemed simple but it doesn't match the books answer.

*my bad posted in wrong forum, if a mod wants to move this go ahead
 
This should be in the homework forum. How about showing us your work, this is an extremely easy problem since it is already exact.

Hint you can directly integrate.
 
footballxpaul said:
(2x-y)dx+(2y-x)dy=0 y(1)=3

solve the given initial value problem and determine at least approx where the solution is valid?


this should be simple right? I got 2y+2x=C and then 2y+2x=8. It doesn't match the answer in the back of the book at all, and I do see how they could have gotten the answer in the back. Is my answer right? The book says y=[x+sqrt(28-3x^2)]/2, abs(x)<sqrt(28/3)? or is the book right, and if so how do you get to their answer?
If 2y+ 2x= 8, then y= 4- x dy= -dx so (2x-y)dx+ (2y-x)dy= (2x- 4+ x)dx+ (8- 2x- x)(-dx)= (3x- 4)dx- (8- 3x)dx= -12, not 0. Your solution is clearly wrong.

Now, how did you get that?

As djeitnstine said, this is an "exact" differential equation that can be integrated relatively easily.
 
Indeed, not even the solution is incorrect. I worked it out this morning...however even without working it out its clear the solution seems extraneous.

Edit: both the OP's solution and the one you claim to have found in the book.
 

Similar threads

Undergrad Understanding Euler Method: Finding Initial Condition of y(0)=1
  • · Replies 7 ·
Replies
7
Views
5K
MHB Can You Solve This System of Differential Equations with Initial Values?
  • · Replies 8 ·
Replies
8
Views
2K
MHB -2.2.12 IVP y'=2x/(y+x^2y), y(0)=-2
  • · Replies 2 ·
Replies
2
Views
2K
MHB -2.1.1 DE Find the general solution
  • · Replies 5 ·
Replies
5
Views
2K
MHB 3.1.11 find the solution of the given initial value problem:
  • · Replies 4 ·
Replies
4
Views
2K
MHB -b.2.2.26 IVP min value y'=2(1+x)(1+y^2); y(0)=0
  • · Replies 3 ·
Replies
3
Views
2K
MHB 2.2.5 de equation with y(1)=1/2
  • · Replies 4 ·
Replies
4
Views
1K
MHB 2.1.7 Find the solution of the given initial value problem.
  • · Replies 1 ·
Replies
1
Views
2K
MHB -1.1.1c Solve for the following initial value
  • · Replies 5 ·
Replies
5
Views
2K
MHB Solving an Initial Value Problem Analytically
  • · Replies 5 ·
Replies
5
Views
2K