Unravelling the Difference Between y' = sin(y) and y' = 2 + sin(y)

  • Thread starter epheterson
  • Start date
  • Tags
    Difference
In summary, the individual added the function y' = 2 to the original function y' = sin(y) and plotted them both in Converge. They noticed that adding the constant 2 caused a rotation and an increase in the slope of the graph. This is due to the non-uniform increase in the slopes caused by the added constant. The periodicity of the field and the odd field transformation can also make it appear as if the graph is rotating and translating.
  • #1
epheterson
22
0
You might want to use converge to help me out with this one, or maybe you know off the top of your head.

I'm trying to determine how

y' = sin(y)

is different from

y' = 2 + sin(y)


I plotted them both in Converge and I don't understand how adding a two rotated and skewed the graph.

Can you explain to me however possible what is going on here?
 
Physics news on Phys.org
  • #2
Or check out the attachment, I watched it while adding increments of .5 until I got up to y'=sin(y) + 2

It seems like every time you add a greater number, you increase the slope a little more. And past the point of y=sin(y) + 1, there are no more equilibrium solutions, it becomes monotonous.


Help?

I attached a word document with all the graphs from Converge
 

Attachments

  • sin(y)+c.doc
    68 KB · Views: 224
  • #3
Well, think about it.

It will rotate it because every slope becomes steeper, correct? Slopes that were 1 are now 3. That's a significant rotation.

It's looking translated is probably a coincidence. What really happened was an increasing of the slopes... and not a uniform one, at that.

So it's not really rotating or translating, although the periodicity of the field and the and the odd field transformation is making it look like that.
 
  • #4
I understand completely now, thanks
 

1. What is the difference between y' = sin(y) and y' = 2 + sin(y)?

The main difference between these two equations is that y' = sin(y) involves a variable (y) and its derivative (y'), while y' = 2 + sin(y) is a constant (2) plus a variable (sin(y)) and its derivative (y'). In other words, the first equation describes a relationship between a function and its derivative, while the second equation describes a relationship between a constant and a function and its derivative.

2. Can both equations be solved analytically?

Yes, both equations can be solved analytically using calculus techniques. The first equation, y' = sin(y), can be solved using separation of variables, while the second equation, y' = 2 + sin(y), can be solved using the trigonometric substitution method.

3. What are the implications of the different equations?

The implications of the different equations depend on the context in which they are being used. In general, the first equation (y' = sin(y)) may describe a physical or natural phenomenon, while the second equation (y' = 2 + sin(y)) may represent a simplified mathematical model or an approximation.

4. Can the solutions of these equations be graphically compared?

Yes, the solutions of these equations can be graphically compared by plotting the corresponding curves on a graph. The solution to y' = sin(y) will be a sinusoidal curve, while the solution to y' = 2 + sin(y) will be a shifted sinusoidal curve.

5. How can these equations be applied in real-world scenarios?

These equations can be applied in various real-world scenarios, such as in physics to describe the motion of a pendulum (y' = sin(y)) or in economics to model the growth of a population (y' = 2 + sin(y)). They can also be used in engineering, biology, and other fields where mathematical modeling is necessary to understand and predict natural phenomena.

Similar threads

MHB B.2.2.16 IVP of \dfrac{x(x^2+1)}{4y^3}, y(0)=-\dfrac{1}{\sqrt{2}}
    • Differential Equations
Replies
6
Views
1K
MHB How to get a converging solution to a second-order PDE?
    • Differential Equations
Replies
1
Views
1K
A How to get a converging solution for a second order PDE?
    • Differential Equations
Replies
3
Views
2K
Modeling a mass falling from one side of the Earth to the other
    • Introductory Physics Homework Help
Replies
1
Views
191
MHB -b.1.3.1 Determine order x^2 \frac{d^2y}{dx^2 }+x\d{y}{x}+2y=\sin\left({x}\right) is linear
    • Differential Equations
Replies
1
Views
1K
I Partial derivatives of the function f(x,y)
    • Calculus
Replies
6
Views
1K
Rotation matrix of three intrinsic rotations
    • Mechanical Engineering
Replies
3
Views
451
A Interpretation of Lagrangian solution (complex numbers)
    • Mechanics
Replies
2
Views
606
3d plot of interference from 2 wave sources with 2d grid surface
    • Programming and Computer Science
Replies
2
Views
1K
I Poisson's inhomogeneous PDE and its solutions
    • Differential Equations
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top