Question

solve (d²+6d)y=x² ans plssss​

Answer 1

Step-by-step explanation:

Given, (D

2

−6D+9)y=x+e

2x

The characteristic equation

p

2

−6p+9=0

⇒(p−3)(p−3)=0

⇒p=3,3 ....(real and equal roots)

C.F. (A+Bx)e

3x

P.I

1

=C

0

+C

1

x

⇒(D

2

−6D+9)(C

0

+C

1

x)=x

⇒−6C

1

+9C

0

+9C

1

x=x

⇒−6C

1

+9C

0

=0

⇒9C

1

=1; 9C

0

=

3

2

⇒C

1

=

9

1

;C

0

=

27

2

⇒P.I.=(

9

x

+

27

2

)

⇒P.I

2

=

D

2

−6D+9

1

e

2x

=

4−−12+9

1

e

2x

=e

2x

The general solution is

y=(A+