Solve the following initial value problem. St/2 if 0 <t<6 y" +y= 3 ift > 6 6 y(0) = y'(0) = 0 14Pm1011* 1917 Prid A++ V "Top14
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
Question 4 < > Solve the initial value problem below. x+y'' - xy' + y = 0, y(1) = – 5, y'(1) = 0 y
Question 4 < > Solve the initial value problem below. xʻy" – xy' +y = 0, y(1) = – 5, y'(1) = 0 =
(1 point) Solve the initial value problem 10 10(+ 1) My – by = 241, 24t. for t> -1 with y(0) = 3. y=
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?
differential equations Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
Solve the initial-value problem shown below: +3; y(-2) =1. Give an exact formula for y. Please assume that > > -3, and use this assumption to simplify any absolute values that may occur. SE y =
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
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.