Help finding general solution for 2nd order linear DE

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Homework Help Overview

The discussion revolves around finding the general solution for the second-order linear differential equation: t²y'' - 2y = 0. Participants are exploring the implications of the equation and its relationship to previously provided functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants express confusion regarding the term t² in the equation and seek guidance on how to approach the problem. Questions are raised about the relevance of previously given functions y1(t) and y2(t) and their connection to the current problem. There is also a discussion about the form of the solution and the correct independent variable.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the relationship between the given functions and the differential equation. Some have suggested a potential form for the solution, but there is no explicit consensus on the correctness of this approach or the next steps to take.

Contextual Notes

Participants note that the independent variable is t, not x, which has led to some confusion in the formulation of the solution. There is also mention of initial conditions provided in the problem statement, but their relevance is still being assessed.

Jende
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Homework Statement


Find the general solution for the DE: t2y''-2y=0

Homework Equations


These were given for other parts of the problem so I'm not sure if they're relevant.
y1(t)=t2, y2(t)=t-1, y(1)=-2, y'(1)=-7

The Attempt at a Solution


The t2 at the front was really stumping me and I'm not sure where to begin.

Thanks in advance for any help.
 
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Jende said:

Homework Statement


Find the general solution for the DE: t2y''-2y=0

Homework Equations


These were given for other parts of the problem so I'm not sure if they're relevant.
y1(t)=t2, y2(t)=t-1, y(1)=-2, y'(1)=-7

The Attempt at a Solution


The t2 at the front was really stumping me and I'm not sure where to begin.

Thanks in advance for any help.

The earlier parts are relevant. What are ##y_1(t)## and ##y_2(t)##? That is, what do they have to do with this problem? Once you answer that, what do you know about solutions of linear equations?
 
LCKurtz said:
The earlier parts are relevant. What are ##y_1(t)## and ##y_2(t)##? That is, what do they have to do with this problem? Once you answer that, what do you know about solutions of linear equations?

So it should come out to be: y(x)=C1t2+C2t-1
 
Jende said:
So it should come out to be: y(x)=C1t2+C2t-1

So what should come out that? And does it?
 
Jende said:
So it should come out to be: y(x)=C1t2+C2t-1
The independent variable is t, not x, so the above should be y(t)=C1t2+C2t-1
 

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