Solve the following ODE by using the Laplace transform y'(x)-8y(x)=0 y(0)=e

Reggie

Reggie

Answered question

2020-12-05

Solve the following ODE by using the Laplace transform
y(x)8y(x)=0
y(0)=e

Answer & Explanation

Cullen

Cullen

Skilled2020-12-06Added 89 answers

Step 1
To solve the given differential equation:
y(x)8y(x)=0
y(0)=e
Step 2
Solve this using Laplace transform, as:
L{y(x)8y(x)}=L{0}
(y8)Y(s)=0
(And, L{0}=0)
[sY(s)y(0)]8Y(s)=0
Substitute y(0)=e
sY(s)e8Y(s)=0
(s8)Y(s)=e
Y(s)=es8
Step 3
Now, using inverse Laplace transformation:
y(t)=L1{Y(s)}
=L1{es8}(t)
=eL1{1s8}(t)
=e1e8x=e1+8t
Thus, solution of given initial value problem is
y(t)=e1+8t

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