# Find the general solution to the homogeneous differential equation d^2 y / d t^2 - 6 d y / d t =...

## Question:

Find the general solution to the homogeneous differential equation {eq}\frac{d^2 y}{d t^2} - 6 \frac{d y}{d t } = 0.{/eq}

The solution can be written in the form {eq}y = C_1 e^{r_1 t} + C_2 e^{r_2 t} {/eq}

with {eq}r_1 < r_2 {/eq}

Using this form, {eq}r_1 = \ and \ r_2 = {/eq}

## IHomogeneous Differential Equation:

The given second-order homogeneous differential equation can be solved by finding the roots of the auxiliary equation. Two linearly independent solutions are found out and their linear combination forms the complete solution to the given differential equation.