A hall has four walls, each measuring 11.5×7.2 it has two doors of height 2m and weight 1m . it also has three windows of size 1m×0.5. find the cost of whitewashing the walls at the rate of ruppes 65 per square metre.​

Answer:

The general solution of the ordinary differential equation can be given by

y

(

x

)

=

C

.

F

.

+

P

.

I

.

y(x)=C.F.+P.I., where

C

.

F

.

C.F. is a complementary function and

P

.

I

.

P.I. is a particular solution. For the general solution of the differential equation, find out the

C

.

F

.

C.F. by taking the auxiliary equation. We can use the normal form method or the variation of parameters method to find out the particular solution of the differential equation.

Answer and Explanation: 1

Take

d

d

x

=

D

ddx=D. So, the given equation is

D

2

y

−

6

D

y

+

9

y

=

x

−

3

e

3

x

D2y−6Dy+9y=x−3e3x.

Simplify the left side of the obtained equation.

(

D

2

−

6

D

+

9

)

y

=

x

−

3

e

3

x

(D2−6D+9)y=x−3e3x

Find out the

C

.

F

.

C.F. by taking the auxiliary equation, that is,

m

2

−

6

m

+

9

=

0

m2−6m+9=0.

m

2

−

6

m

+

9

=

0

m

2

−

3

m

−

3

m

+

9

=

0

m

(

m

−

3

)

−

3

(

m

−

3

)

=

0

(

m

−

3

)

(

m

−

3

)

=

0

m2−6m+9=0m2−3m−3m+9=0m(m−3)−3(m−3)=0(m−3)(m−3)=0

m

−

3

=

0

m

=

3

m−3=0m=3

m

−

3

=

0

m

=

3

m−3=0m=3

As the roots are real and equal,

C

.

F

.

=

(

c

1

+

x

c

2

)

e

3

x

C.F.=(c1+xc2)e3x.

Now, find out the particular solution of the given equation,

P

.

I

.

=

1

D

2

−

6

D

+

9

x

−

3

e

3

x

P.I.=1D2−6D+9x−3e3x.

P

.

I

.

=

1

D

2

−

6

D

+

9

x

−

3

e

3

x

=

1

(

D

−

3

)

2

x

−

3

e

3

x

=

e

3

x

1

(

(

D

+

3

)

−

3

)

2

x

−

3

=

e

3

x

1

(

D

+

3

−

3

)

2

x

−

3

=

e

3

x

1

D

2

x

−

3

=

e

3

x

1

D

(

1

D

(

x

−

3

)

)

=

e

3

x

1

D

(

x

−

2

−

2

)

=

−

e

3

x

2

1

D

(

x

−

2

)

=

−

e

3

x

2

(

x

−

1

−

1

)

=

e

3

x

2

x

P.I.=1D2−6D+9x−3e3x=1(D−3)2x−3e3x=e3x1((D+3)−3)2x−3=e3x1(D+3−3)2x−3=e3x1D2x−3=e3x1D(1D(x−3))=e3x1D(x−2−2)=−e3x21D(x−2)=−e3x2(x−1−1)=e3x2x

Substitute the obtained values of

C

.

F

.

C.F. and

P

.

I

.

P.I. into the equation

y

(

x

)

=

C

.

F

.

+

P

.

I

.

y(x)=C.F.+P.I..

y

(

x

)

=

(

c

1

+

x

c

2

)

e

3

x

+

e

3

x

2

x

y(x)=(c1+xc2)e3x+e3x2x

Thus, the general solution of the given differential equation is

y

(

x

)

=

(

c

1

+

x

c

2

)

e

3

x

+

e

3

x

2

x

y(x)=(c1+xc2)e3x+e3x2x.

Explanation:

was this helpful?

Step-by-step explanation:

Correct option is A)

Given,

x² −x(a+b)+k=0

x=a

⇒a²−a(a+b)+k=0

a²−a²−ab+k=0

∴k=ab

Given,

ab/k= ab/aa=1

Answer:

i think have petrr or john told

Answer:

Have Peter or John told you the story?

Explanation:

Have is used since more than one subject is used to address.

I hope this is the answer!!☺️

Answer:

from 8064 - 143

we have perfect square

Answer:

8064-163 अगर ताल्लुक हो तो रूह से रूह का हो,

दिल तो अक्सर एक दूसरे से भर जाते हैं।

मुझ को मज़ा है छेड़ का दिल मानता नहीं,

गाली सुने बगैर सितमगर कहे बगैर।

कौन सी बात नई ऐ दिल-ए-नाकाम हुई,

शाम से सुबह हुई सुबह से फिर शाम हुई।

जिद भी की दिल ने तो इश्क करने की,

आज कहता है कि तूने मुझे रोका भी नहीं।

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