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

x = 12

y = 15

step-by-step explanation: