Question 7 < > Solve the initial-value problem using the Method of Undeterminded Coefficients: y' +...
cometeness and clarity please ! 1. Solve the initial value problem using Laplace transforms. ſi ost<5 y" - 5y + 4y = 0 t25 y(0) = 0, 7(0) = 1
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 =
4. Use the Laplace transform to solve the initial value problem y" + y = f(1) = -2, ost<2 13t+4, 122 y(0) = 0, y'(0) = -1
So 0<t<5 Using the Laplace transform, solve the initial value problem y' + y = 3 t5 y'(0) = 0. 9
Use the Laplace transform to solve the given initial-value problem. so, 0 <t< 1 y' + y = f(t), y(0) = 0, where f(t) 17, t21 y(t) = + ult-
QUESTION 3 Use Laplace Transform to solve the initial value problem y" + 9y = f(t) ,y(0) = 1, y'(0) = 3 where 6, f(t) 0 <t<nt i < t < 0
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 =
Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem has a unique solution. b) Compute (by hand) an approximation of y(3) using the forward Euler method with a step size h = 0.5 (namely perform 2 steps of the method).