Answer:

Explanation:
Given differential equation,


Since, the above equation is of the type of linear differential equation
,
In which P = -3, Q =
,
Thus, the integrating factor,

Hence, the solution of the given differential equation would be,




Let,

Integrating by parts, ( First term = sin t, second term =
)

![I=-(e^(-3t) sint)/(3) - [(e^(-3t) cost )/(9)-\int -(e^(-3t) sint)/(9)dt]+C](https://img.qammunity.org/2020/formulas/mathematics/college/8x9aq1dk8ghl5mk1pngzyzw5mpmj2tkx8n.png)
![I=-(e^(-3t) sint)/(3) - [(e^(-3t) cost )/(9)+(1)/(9)\int e^(-3t) sint dt]+C](https://img.qammunity.org/2020/formulas/mathematics/college/bauxmk3gry68ip0bgk4n6pd8dtu4gsqvh9.png)
( from equation (2))


( where, C' = 9C/10 )

From equation (1),

