Question

..
Solve using Laplace transformation
y" +4y'-5y=5, given y = 0, y = 2 at t = 0.
t=0
எனும்போது
y =0, y' = 2
எனில்
y" +4y'-5y = 5 லாப்லாஸ் உருமாற்றம் கொண்டு தீர்க்க.
5
272​

Answer 1

Answer:

I have the following problem

y′′+4y′+5y=δ(t−1),y(0)=0,y′(0)=3

When transforming I get

s2Y−sy(0)−y′(0)+4(sY−y(0))+5Y=e−sY(s2+4s+5)=e−s+3Y(s)=e−s+3s2+4s+5

Now, I rewrote s2+4s+5=(s+2)2+1

Y(s)=e−s(1(s+2)2+1)+3(1(s+2)2+1)

And transforming back I use the fact that eatsinbt=L−1(b(s−a)2+b2) thus I get

y(t)=δ(t−1)e−2tsint+3e−2tsint

Explanation: