If y1(t)=e^3t and y2(t)=e^−3t are solutions to y''−9y=0, what is the general solution?

Question

If y1(t)=e^3t and y2(t)=e^−3t are solutions to y''−9y=0, what is the general solution?

Answer 1

If y1(t) = e^(3t) and y2(t) = e^(-3t) are solutions to the differential equation y'' - 9y = 0, then the general solution is a linear combination of these two solutions.

That is,

y(t) = C1 * e^(3t) + C2 * e^(-3t),

where C1 and C2 are constants determined by initial conditions or boundary conditions.