So it would be in six years because if you do it, it would be
garden 1: 2,4,6,8
garden 2: 3,6,9
and the lowest common multiple is 6 so in 6 years is when it will happen again
The general form of a solution of the differential equation is already provided for us:

where
. We now want to find a solution
such that
and
. Therefore, all we need to do is find the constants
and
that satisfy the initial conditions. For the first condition, we have:
For the second condition, we need to find the derivative
first. In this case, we have:

Therefore:

This means that we must solve the following system of equations:

If we add the equations above, we get:

If we now substitute
into either of the equations in the system, we get:

This means that the solution obeying the initial conditions is:

Indeed, we can see that:


which do correspond to the desired initial conditions.
Divide all the terms by 2:
2xy + 12z + 3xy - z