+ 2y = 4u, y(0) = 0, for the following input: Solve: dt 0<t<T u(t) t>T Graph the solution (you may use Excel or Matlab) for T= 1sec, 0.1sec, 0.01sec, and 0.001sec. Do you see what is happening to the output? What is happening to the input?!
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a. Given that yı(t) = 3t is a solution, apply the reduction of order method to find another solution y2 for which yı and y2 form a fundamental solution set. i. Starting with yi, solve for w in yıw' + (2y + p(t)yı)w = 0 so that w(1) = -3. w(t) = ii. Now solve for u where u = w so that u(1) =...
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5 St<20 10, 0<t<5 and t > 20
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t- dt - 6y = 0 dt² The general solution is y(t) =
Let f(x, y) 2e-(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFS of each?
Let f(x,y) = 12e-2(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFs of each?
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where xo + 0, b) no solution exists if y (0) = yo # 0, and c) an infinite number of solutions exist if y (0) = 0.
Solve the differential equation by variation of parameters. Y"' + 3y' + 2y = 6 > 9+ et
Find the general solution or particular solution of each the following DE's 1) (y-y2 tanx)dx + (2y+tanx)dy=0 2) (x2+y2+x)dx + xydy-0 i y(-1)-1 4) For the initial value problem y' + xy - xy? ex2 ; y(0)-1 Find the explicit solution if y>0 dy dae dy
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6