Differential equations true/false question

[freshman2013]

Homework Statement

If y1 and y2 are solutions to y"-y = 0 then c1y1+c2y2 represent all solutions to the differential equation for all scalars c1 and c2

Homework Equations

The Attempt at a Solution

Basically, my TA's solutions to his worksheet said it was true, and I'm not sure if he implied that y1 and y2 are linearly independent solutions, since in that case it would definitely be true. I'm not sure if I got the vocab mixed up or something. (y1 can be e^x and y2 can be 2e^x and that would make my original question false, right?)

 

[LCKurtz]

Homework Statement

If y1 and y2 are solutions to y"-y = 0 then c1y1+c2y2 represent all solutions to the differential equation for all scalars c1 and c2

Homework Equations

The Attempt at a Solution

Basically, my TA's solutions to his worksheet said it was true, and I'm not sure if he implied that y1 and y2 are linearly independent solutions, since in that case it would definitely be true. I'm not sure if I got the vocab mixed up or something. (y1 can be e^x and y2 can be 2e^x and that would make my original question false, right?)

You have it exactly right. Unless the two solutions are linearly independent the answer is "false".