Question

Find the real-valued general solution to the differential equation z" - 6z' = 0. z(t) = (use constants a, b, etc., for any constants in your solution formula.)

Answer 1

The general solution of the given differential equation z'' - 6z' = 0 is z(t) = a + bt, where a and b are constants.

Step-by-step explanation:

The given differential equation is z'' - 6z' = 0.

To find the general solution, we can rewrite the equation in terms of the derivative notation: r^2 - 6r = 0, where r represents dz/dt.

Factoring out r, we have r(r - 6) = 0. Therefore, r = 0 or r = 6.

The general solution is z(t) = a + bt, where a and b are constants.