Solve the following simultaneous DE using Laplace transforms. 1. dx 2 + dy dt Бет = dt dy · 3 d = 5 given that when t = 0, x = 0 and y = 0. dt 2.

dy Find dt y (2+ cos 4t) dy dt.

2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?

find dy ах Sin(xy) = sinx +sing dy [sin(ry)] = = [simx + Simy] dx dx