Average speed = (distance final - distance initial)/(time final - time initial)
Average speed = (30-0)km /(100 -0)min = 3/10 km/min
3/10 km/min *60 min/1 h = 180/10 km/h= 18 km/h
Let

. Then

and

are two fundamental, linearly independent solution that satisfy


Note that

, so that

. Adding

doesn't change this, since

.
So if we suppose

then substituting

would give

To make sure everything cancels out, multiply the second degree term by

, so that

Then if

, we get

as desired. So one possible ODE would be

(See "Euler-Cauchy equation" for more info)
we know that
the perimeter of the rectangle is equal to

where
P is the perimeter of the rectangle
W is the width of the rectangle
L s the length of the rectangle
In this problem

Substitute the values in the formula above


therefore
the answer is
the length of the longer side of the rectangle is equal to 