Solve the following equation with Laplace Transform Method (Inverse Laplace the equation to find the solution) y"-3y'-4y=3e^{2x} y(0)=1 , y'(0)=0

Amari Flowers

Amari Flowers

Answered question

2021-02-06

Solve the following equation with Laplace Transform Method (Inverse Laplace the equation to find the solution)
y"3y4y=3e2x
y(0)=1,y(0)=0

Answer & Explanation

pattererX

pattererX

Skilled2021-02-07Added 95 answers

Step 1
Given differential equation,
y"3y4y=3e2x
y(0)=1,y(0)=0
Solve this differential equation by Laplace Transform method.
Step 2
y"3y4y=3e2x
Take Laplace Transform of both sides,
L[y"3y4y]=L[3e2x]
L[y"]3L[y]4L[y]=3L[e2x]
Use the formula such that 
L[y"]=s2L[y]sy(0)y(0)
L[y]=sL[y]y(0)
L[eax]=1sa
Then from (1),
Step 3
s2L[y]sy(0)y(0)3[sL[y]y(0)]4L[y]=3×1s2
s2L[y]s×103[sL[y]1]4L[y]=3s2
{s23s4}L[y]=3s2+s3
L[y]=3(s2)(s23s4)+s3s23s4
y=L1[3(s2)(s23s4)+s3s23s4]
y=3L1[1(s2)(s23s4)]+L1[s3s23s4]...(2)
Step 4
Now
1(s2)(s23s4)=16(s2)+115(s+1)+110(s4)
L1[1(s2)(s23s4)]=L1[16(s2)]+L1[115(s+1)]+L1[110(s4)]

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?