Question

(D^2+1)y=x^3+e^-x+e^xsinx
​

Answer 1

Answer:

Step-by-step explanation:

D+1)(D+3)y=e

−x

sinx+xe

3x

C.F. = C

1

​

e

−x

+C

2

​

e

−3x

For P.I. , we get

D

2

+4D+3

e

−x

sinx+xe

3x

​

e

−x

 

D(D+2)

sinx

​

+e

3x

 

(D+4)(D+6)

x

​

e

−x

 

D(D

2

−4)

(D−2)sinx

​

+e

3x

 

24

24

(D

2

+10D)

​

+1

x

​

=e

−x

 

−3

(sinx+2cosx)

​

+e

3x

 

288

5

​

Answer 2

this your answer hope it have you