Basis for the space of solutions (ODE)

[Poetria]

Homework Statement

The equation given:

dy/dt = 3*y

A basis for the space of solutions is required.

The Attempt at a Solution

According to me it is e^(3*t) but it has turned out false. Why? I am considering the answer "The basis is the set of all functions of the form c*e^(3*t) but a different example was described as follows:
"The vector space of solutions to a homogeneous ODE consists of infinitely many functions. To describe it compactly, we give a basis of the vector space. In this case, the basis has only 2 functions."

Is it possible that my answer is correct and there is a bug here?

 

[member 587159]

Homework Statement

The equation given:

dy/dt = 3*y[/B]

A basis for the space of solutions is required.

The Attempt at a Solution

According to me it is e^(3*t) but it has turned out false. Why? I am considering the answer "The basis is the set of all functions of the form c*e^(3*t) but a different example was described as follows:
"The vector space of solutions to a homogeneous ODE consists of infinitely many functions. To describe it compactly, we give a basis of the vector space. In this case, the basis has only 2 functions."

Is it possible that my answer is correct and there is a bug here?[/B]

What is their basis? What is the vector space you are working in? Those are essential things to know.

You are right to say that $y(t) = Ae^{3t}$ is the solution of this differential equation.

 

[LCKurtz]

Homework Statement

The equation given:

dy/dt = 3*y[/B]

A basis for the space of solutions is required.

The Attempt at a Solution

According to me it is e^(3*t) but it has turned out false. Why? I am considering the answer "The basis is the set of all functions of the form c*e^(3*t) but a different example was described as follows:
"The vector space of solutions to a homogeneous ODE consists of infinitely many functions. To describe it compactly, we give a basis of the vector space. In this case, the basis has only 2 functions."

Is it possible that my answer is correct and there is a bug here?[/B]

You are correct that the function $e^{3t}$ is a basis for the solution space. Perhaps the problem is typing it in a particular format for an online problem? Maybe they want something like $\{e^{3t}\}$. In any case, you do understand it correctly.

 

[Poetria]

You are correct that the function $e^{3t}$ is a basis for the solution space. Perhaps the problem is typing it in a particular format for an online problem? Maybe they want something like $\{e^{3t}\}$. In any case, you do understand it correctly.

Many thanks. :) It is the main thing to understand it correctly. :) I will ask if this is a technical problem with a grader.

 

[LCKurtz]

Many thanks. :) It is the main thing to understand it correctly. :) I will ask if this is a technical problem with a grader.

I will guess that they want the set notation, since a basis is a set of functions. In this case, a set containing a single function.

 

[Poetria]

I will guess that they want the set notation, since a basis is a set of functions. In this case, a set containing a single function.

I can only tick 'one', 'two' etc. I can't add the set notation. Perhaps 'none' of possibilities is the right answer. :) This is annoying.