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.

ratio is 2 : 9

the answer is three

13.5 : 3