For the initial value problem, compute the first two approximations u, and uz given by Euler's method using the given time step. y'(t) = 6y. y(0) = 6; At = 0.5 O A. U1 = 24; U2 = 96 O B. uq = 24; U, = 168 O C. U1 = 42; U2 = 168 O D. U1 =6; U2 = 24Does the function t] = die 5t 1if'ltll Stilt}: 01 will} = '1 satisfy the following initial value problem? {:3 Choose the correct answer below. Yes, because the initial condition satises the original function, so the original function must satisfy the initial value problem. No, because the initial condition does not satisfy the original function, so the original function cannot satisfy the initial value problem. No, because when 3i and y' are substituted into the equation, the result is not a the statement. 0000 Yes, because when yr and y" are substituted into the equation, the result is a tnie statement. Consider the differential equation. A detailed direction field is not needed. Find the solutions that are constant, for all t2 0 (the equilibrium solutions). In what regions are solutions increasing? Decreasing? y'(t) = y(y + 2)(8 -y) O A. y= - 2, y = 8; increasing for y 8 O B. y=0, y= - 2, y= 8; increasing for y 8 O C. y= - 2, y= 8; increasing for - 2 8 O D. y=0, y= - 2, y = 8; increasing for - 2 0Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable. dy dx = y (5x2 + 4) V=