Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
differential equations Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
if t < 41 8(t) = 41 if t > 41 Solve the differential equation y(0) = 6, 7(0) = 5 y" +4y = g(t), using Laplace transforms. ift < 41 if t > 411
Problem 1 Solve y + 4y 1, if 0<t<T, y(0) = 0, y'() = 0. if <t<oo.'
ſi, if 0 St<T, y" + 4y = 10, if a St< 0. y(0) = 0, y(0) = 0. 9
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
Question 2 < > Solve y"' + 4y' + 8y = 0, y(0) = 1, y'(0) = 6 g(t) = The behavior of the solutions are: O Steady oscillation O Oscillating with decreasing amplitude o Oscillating with increasing amplitude
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
Laplace transform of the unit step function y" + 4y = ſi, if 0 <t<, y(0) = 0, y'(0) = 0. 10, if a St<oo.'