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## Main Question or Discussion Point

Something has been bothering me. I see a phrase like this:

Plugging our two roots into the general form of the solution gives the following solutions to the differential equation.

y_1 = ae^xt and y_2 = be^vt

So here we have 2 solutions, I assume, since the text calls them solutions.

It goes on to say, "superposition: c_1 y_1 + c_2 y_2 is also a solution, for any constants"

So not it seems we have 3, or actually infinity if any constant can be used, solutions.

Further, my teacher says that certain DEs can only have one solution. Then he goes on to use these techniques, which define solutions in these different forms!

Please, clear this up for me!

Thank you

Plugging our two roots into the general form of the solution gives the following solutions to the differential equation.

y_1 = ae^xt and y_2 = be^vt

So here we have 2 solutions, I assume, since the text calls them solutions.

It goes on to say, "superposition: c_1 y_1 + c_2 y_2 is also a solution, for any constants"

So not it seems we have 3, or actually infinity if any constant can be used, solutions.

Further, my teacher says that certain DEs can only have one solution. Then he goes on to use these techniques, which define solutions in these different forms!

Please, clear this up for me!

Thank you