Use Euler's method with step size 0.3 to estimate y(0.6), where y(x) is the solution of the initial-value problem y = 3x + y², y(0) y(0.6) = y(0) = -1.

Use the method of undetermined coefficients to find a particular solution to y'' – 9y' + 20y = 3et Yp(t) =

Find a particular solution of Yp(x) y"-2y+y = e(2 - 12x)

The initial condition was at time 0 there was 4 inches of snow (h(0)=4), and with our snowfall rate of 3/5 and snow removal rate of 9/20h the LOWEST the height of snow on the ground could go is 4/3 inches. But i'm wondering, given our initial condition of h(0)=4, Is there any combination of snowfall rate and snow removal rate that could allow the height of snow on the ground to approach zero? For instance, if we made our equation dH/dt=(1/5)-(4/5)*h we could get the lowest snow height to under half an inch...but are there any conditions in which we could get it to approach zero? If not, what's the lowest we could get it and the process for finding such a value? Please explain. Thank you