Question

Find the two values of k for which y(x)=ekx is a solution of the differential equation

Answer 1

Answer:

The 2 values of k are 3 and 6.

Step-by-step explanation:

If the given function  of y is a solution of the differential equation then it shall be able to satisfy it

Thus we have

$y''-9y'+18y=0$

Putiing $y=e^{kx}$ in the above differential euation we get

$\frac{d^2e^{kx}}{dx^2}-9\frac{de^{kx}}{dx}+18\cdot e^{kx}=0\\\\k^{2}e^{kx}-9k\cdot e^{kx}+18\cdot e^{kx}=0\\\\k^2-9k+18=0$

Solving the above uadratic euation with the standard formula we get

$k=\frac{-(-9)\pm \sqrt{(-9)^2-4\times 1\times 18} }{2}\\\\k_1=6\\\\k_2=3$