Use the laplace transformation to solve the given ivp.
y'-y=2sin3t, y(0)=0

Step-by-step explanation:

We are given that

y'-y=2 sin3t,y(0)=0

We have to solve given differential  equation using Laplace transform

We know that L(y'-y)=L(2sin3t)

Using partial fraction

s-1=0 then s=1

substitute s= 1 in equation

6=A(1+9)

Comparing coefficient of and s on both sides then we get

Substitute the values

Then, Y(s)=

Apply inverse transform then we get

and

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.