Question

Solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution. W'+w=30(t - 3) - 4u{t-5); (C)= 2, w'(C)=0 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem wt) - Sketch the graph of the solution A. ОВ. OD oc AY 104 Ay AY 10- 10- 10 A

Answer 1

w"tw. -58 4 e 28 (32-33 .4e5s + 2 3+1 Taking А 871 + B 8 --- - 346-3)-4 u(+-5) ---6) WO)-2, w(0) = 0 Taking Laplace transfrom on both sides we get L { wo} +2{w} = '3 2 { ult-2)} -4L?u(8-5)} = $ {w} - WO)-, W'10) +L{w} = 3.0-38 2 (878) L{w} - 28-0 = 1 (30-38-4e-5s) 9 e{w} 3-46-58)+ 3(878) $18 3 e34_4 ) {W} inverse haplace trans from both sides we get w (t) = 34' {$**')} - green } + 21{37 {3+1}. ti) Let 8(811) $2 - 1 7 A8+B 8 (871) +C .(8+1) 7. Putting R = 0,11 get and 1= A A+2B +20=1+ 2B +2=1:-) B=-1. :) $(3+) : f (t) = L Lt 879+1)] 13-2"{}}+{'{}} f(x) - 1 tt in from & we get w(t) = 3 u(+-3) f(4-3) – 4 06-5)f(+-5)+267 2 w(4)= 3[e*+3+14-3)-1] u(4-3)-45€ **574-5)-1] 468-7)+zet 3 WCH): 3 [e3*+7-4] u(-3)-4 [25***-6]u[4-5)+ze+ 1 1 1 1 sti + 1 1 $+) •t е. -