Suppose that we use Euler's method to approximate the solution to the differential equation 25 dy dx The exact solution can also be found using separation of variables. It is y(x) = y Thus the actual value of the function at the point x = 1.1 y(1.1) = S Let f(x, y) = x³/y. We let zo = 0.1 and yo = 6 and pick a step size h = 0.2. Euler's method is the the following algorithm. From an and yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing y(0.1) = 6. Xn+1 = xn+h, Complete the following table. Your answers should be accurate to at least seven decimal places. n In Yn 0 0.1 6 |1| 2 3 4 Yn+1 = Yn+h. f(xn, yn).

The differential equation: +b+cx=0 has a solution given by: y = e(A sin ßx + B cos x) where a = -1.04 and 3 = 6.34 If initial conditions are y = 1.27 and dy/dt = 4.31 when x = 0, find the values of 4. Give your answer to 3 decimal places.

A 90 gallon tank initially contains 10 gallons of water and 5 pounds of salt. Salt solution, at 2.5 lb/gal, begins entering the tank at a rate of 4 gal/min. Simultaneously, a 3 gal/min drain is opened. in the bottom of the tank. Let s(t) be the amount of salt in the tank at time t. Find the differential equation and initial condition for which s(t) is a solution. DO NOT SOLVE THE DIFFERENTIAL EQUATION.

Find L{f(t)}. (Write your answer as a function of s.) Re) - { -1, 1, 0 st 0)