3 Determine whether the given set of functions form a fundam

3. Determine whether the given set of functions form a fundamental set of solutions of the differential equation on the indicated interval; that is, they are n solutions of the nth order ODE that are linearly independent:

Solution

c).First oif all y₁ = e^x is not a solution of y\"\' - 4y\" + 4y=0.

y\"\' - 4y\" + 4y= is a linear differential equation of third order.

For its general solution we must have three linealy independent solutions.

First of all they must be solutions.