Use the Laplace transform to solve the given initial-value problem. dy/dt-y=z,\ y(0)=0

pancha3

pancha3

Answered question

2021-08-22

Use the Laplace transform to solve the given initial-value problem.
dydty=z, y(0)=0

Answer & Explanation

diskusje5

diskusje5

Skilled2021-08-23Added 82 answers

Step 1
dydty=1, y(0)=0
dydty=1
L{dydty}=L{1}
L{dydt}L{y}=1s
sY(s)y(0)Y(s)=1s
sY(s)0Y(s)=1s
sY(s)Y(s)=1s
(s1)Y(s)=1s
Y(s)=1s(s1)
y(t)=L1{Y(s)}
=L1{1s(s1)}
=L1{s(s1)s(s1)}
=L1{ss(s1)s1s(s1)}
=L1{1s11s}
=L1{1s1}L1{1s}
=et1
That is
y(t)=et1

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?