Showing that some functions are solutions to a diff eq.

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The discussion centers on verifying that the functions y1(t) and y2(t) are solutions to a specific differential equation. The participant initially questions how to demonstrate this by substituting the functions into the equation. After further reflection, they conclude that taking the derivatives of the solutions and comparing them to the results from the differential equation confirms their validity as solutions. The importance of checking each function separately is emphasized to ensure both satisfy the equation.

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Duderonimous
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Homework Statement


Show that y1(t) and y2(t) are solutions to a certain differential equation.

Homework Equations


The Attempt at a Solution



I plug both of these into my diff. eq. and I got the same thing. How is this showing that they are solutions to a diff. eq.? What if I got a different answer when I plugged in each function, what would that mean?

I omitted the details because I thought this ws more of a concept question. THanks

I think I answered my own question, I took the derivative of the solns and they equaled what I got when I plugged the solns into the diff. eq. :)
 
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You are asking a very general question. Why don't you provide a complete problem statement along with your work?
 
Duderonimous said:

Homework Statement


Show that y1(t) and y2(t) are solutions to a certain differential equation.

Homework Equations





The Attempt at a Solution



I plug both of these into my diff. eq. and I got the same thing.
What do you mean by "got the same thing". The question is whether the two functions separately satisfy the differential equation. When you put y1 into the equation are both sides the same?

How is this showing that they are solutions to a diff. eq.? What if I got a different answer when I plugged in each function, what would that mean?

I omitted the details because I thought this ws more of a concept question. THanks

I think I answered my own question, I took the derivative of the solns and they equaled what I got when I plugged the solns into the diff. eq. :)
 

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