The solutions to the linear differential equation d2u/dt2 = u form a vector space (since combinations of solutions are still solutions). find two independent solutions, to give a basis for that solution space.

Serious high school. This is one of the few differential equations I can solve.

The usual particular solution is because is its own derivative.

An independent solution is which has a negative sign in the first derivative which turns back to positive in the second.

The arbitrary linear combination spans the solution space:

But we only are asked for the basis.

beluga wheeeaaalle matt

step-by-step explanation:

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)