Showing that some functions are solutions to a diff eq.

[Duderonimous]

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. :)

 

[SteamKing]

You are asking a very general question. Why don't you provide a complete problem statement along with your work?

 

[HallsofIvy]

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. :)