Form of Solution for First Order ODE T'(t) - (1 - n^2/4)T(t) = 0

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Homework Help Overview

The discussion revolves around the form of the solution for first-order ordinary differential equations (ODEs), specifically focusing on the equation T'(t) - (1 - n^2/4)T(t) = 0. Participants are examining the correct expression for the solution and exploring related equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the form of the solution for the given ODE, with one questioning the notation used in the book. Another participant raises a different equation, seeking the form of its solution and expressing difficulty in determining solutions for differential equations.

Discussion Status

The discussion includes attempts to clarify the correct form of the solution, with some participants suggesting potential errors in the book's notation. There is also an exploration of a different ODE, indicating a broader inquiry into solving first-order equations.

Contextual Notes

Participants are working within the constraints of homework guidelines, which may limit the depth of exploration into solutions. The original poster's confusion about notation highlights the importance of precise mathematical expression in ODEs.

leopard
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y'(t) - ay(t) = 0

What is the form of the solution? [tex]C \cdot e^{at}[/tex]

?I have this ODE:

[tex]T'(t) - (1 - \frac{n^2}{4})T(t) = 0[/tex]

If I'm right, the solutions should be of the form

[tex]C \cdot e^{(1- \frac{n^2}{4})t}[/tex]

My book, however, says [tex]C \cdot e^ {1- \frac{n^2}{4}t}[/tex]

Who's right?
 
Last edited:
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I think the book forgot some parentheses
 
Brilliant.

And how about the equation

y' = (y - x)^2

what's the form of the solution here?

I find it hard to determine the form of solution of differential equations.
 
Last edited:
I would try a simple substitution first. How about v=y-x? Now see if you can separate it in those variables.
 

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