The DE obtained by eliminating $c_1$ and $c_2$ from $y = c_1 e^{3x} + …

Question

The DE obtained by eliminating $c_1$ and $c_2$ from $y = c_1 e^{3x} + c_2 e^{2x}$ is:

Accepted Answer

A. $d^2y/dx^2 - 5\,dy/dx + 6y = 0$

Characteristic roots 3 and 2 give the auxiliary equation $(D-3)(D-2) = 0$ ⇒ $D^2 - 5D + 6 = 0$, i.e., $d^2y/dx^2 - 5\,dy/dx + 6y = 0$. (Alternative: differentiate twice and eliminate $c_1, c_2$.)

Answer

$d^2y/dx^2 + 5\,dy/dx + 6y = 0$

Answer

$d^2y/dx^2 - dy/dx + 6y = 0$

Answer

$d^2y/dx^2 + 6y = 0$