Laplace transform of the unit step function y" + 4y = ſi, if 0 <t<, y(0) = 0, y'(0) = 0. 10, if a St<oo.'
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
15) 5. Use Laplace transforms to solve the initial value problem y" + y = g(t), y'(0) = 0, y(0) = 0, where 0 St< 10, 10 t 20, 0, g(t) = (t-10), 1, t < 20, and describe the qualitative behavior of the solution fort 20
10. Use the Laplace transform to solve y" - 3y' +2y f(t), y(0)-0,'(0) 0, where (t)-(0 for 0 st < 4; for t 2 4 No credit will be given for any other method. (10 marks)
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
ſi, if 0 St<T, y" + 4y = 10, if a St< 0. y(0) = 0, y(0) = 0. 9
Laplace transform of the unit step function y"+y= St/2, if 0 St<6, 13, if t > 6 y(0) = 6, y'(0) = 8
Problem 2: [Also challenging] Find the solution of the following IVP: y' +2y = g(t), with y(0) = 3 where g(t) = - 0<t<1: g(t) = te-2 > 1.
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
So 0<t<5 Using the Laplace transform, solve the initial value problem y' + y = 3 t5 y'(0) = 0. 9