Ordinary Differential Equations

Click For Summary

Homework Help Overview

The discussion revolves around ordinary differential equations, specifically examining the relationship between a given equation and a proposed solution involving constants.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are exploring whether the proposed solution, involving a square root and a constant, satisfies the original differential equation. There is uncertainty regarding the role of the constant C1 in the context of the equations presented.

Discussion Status

The conversation is ongoing, with participants attempting to clarify the relationship between the equations and the proposed solution. Some guidance has been offered regarding finding derivatives and substituting them back into the original equation.

Contextual Notes

There is mention of confusion regarding the constants and their implications in the equations, as well as a potential misinterpretation of the second equation.

aaronfue
Messages
118
Reaction score
0

Homework Statement



y = 2xy' + y(y')2; y2 = C1 (x + C1 /4)



2. The attempt at a solution

I thought that I could take the first equation and set it equal to zero. But the C1 in the second equation is throwing me off.

Am I supposed to set the second equal to C1?
 
Last edited:
Physics news on Phys.org
Are you saying that you want to show that [itex]y= \pm\sqrt{C_1(x+ \frac{C_1}{4})}[/itex] satisfies [/itex]y= 2xy'+ y(y')^2[/itex]?

Just find the derivative of y and plug it into the equation.
 
HallsofIvy said:
Are you saying that you want to show that [itex]y= \pm\sqrt{C_1(x+ \frac{C_1}{4})}[/itex] satisfies [/itex]y= 2xy'+ y(y')^2[/itex]?

Just find the derivative of y and plug it into the equation.

Sorry the second equation is y2, but I think I see what you are saying.
 
Yes, that's why I took the square root to get y.
 

Similar threads

Linear Differential Equations and Linear Operator Problem
  • · Replies 4 ·
Replies
4
Views
2K
Why can't a critical point of a system of DEs be complex?
  • · Replies 27 ·
Replies
27
Views
2K
Solve a 2nd order Ordinary Differential Equation
  • · Replies 3 ·
Replies
3
Views
2K
Solving Harmonic Oscillation w/ BC y(1)=B
  • · Replies 2 ·
Replies
2
Views
1K
Solve for the solution of the differential equation
  • · Replies 9 ·
Replies
9
Views
2K
Doubt related to formation of a differential equation
  • · Replies 5 ·
Replies
5
Views
2K
Ansatz for particular solution - Inhomogenous diff equation
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Solve the given differential equation
  • · Replies 3 ·
Replies
3
Views
1K
Use of the constant C in the solution of Differential Equations
  • · Replies 18 ·
Replies
18
Views
4K