Christine sleep form 11pm until 9am what fraction of a day does Christine sleep

Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie

melamori03 [73]

Answer:

The complete solution is

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

Step-by-step explanation:

Given differential equation is

3y"- 8y' - 3y =4

The trial solution is

$y = e^{mx}$

Differentiating with respect to x

$y'= me^{mx}$

Again differentiating with respect to x

$y''= m ^2 e^{mx}$

Putting the value of y, y' and y'' in left side of the differential equation

$3m^2e^{mx}-8m e^{mx}- 3e^{mx}=0$

$\Rightarrow 3m^2-8m-3=0$

The auxiliary equation is

$3m^2-8m-3=0$

$\Rightarrow 3m^2 -9m+m-3m=0$

$\Rightarrow 3m(m-3)+1(m-3)=0$

$\Rightarrow (3m+1)(m-3)=0$

$\Rightarrow m = 3, -\frac13$

The complementary function is

$y= Ae^{3x}+Be^{-\frac13 x}$

y''= D², y' = D

The given differential equation is

(3D²-8D-3D)y =4

⇒(3D+1)(D-3)y =4

Since the linear operation is

L(D) ≡ (3D+1)(D-3)

For particular integral

$y_p=\frac 1{(3D+1)(D-3)} .4$

$=4.\frac 1{(3D+1)(D-3)} .e^{0.x}$ [since $e^{0.x}=1$ ]

$=4\frac{1}{(3.0+1)(0-3)}$ [ replace D by 0 , since L(0)≠0]

$=-\frac43$

The complete solution is

y= C.F+P.I

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

4 0

2 years ago

your friend is choosing between two music download companies. MyTunes charges $2.50 per song. Great Songs charges $1.50 per song

vichka [17]

Answer:

After 100 songs

Step-by-step explanation:

2.50x=1.50x+50

.50x=50

÷.50

X=100

4 0

2 years ago

On her math test, Anna got I 32 questions out of 36 | questions correct. About | what percent of the questions did Anna get corr

Scilla [17]

Answer:

%88.88... and on and on

Formula Nonsense: percentage = b/l then *100 add % sign

so P= 32/36 so 0.888....*100= 88.88... so she made 88%

6 0

2 years ago

Diego is solving this system of equations:

USPshnik [31]

The solutions of the equations are x = 1 and y = 2

The system of equations are

4x + 3y = 10

-4x + 5y = 6

Here we have to use the elimination method. Eliminate the x term and find the value of y term

Add both equation

3y + 5y = 10 +6

Add the like terms

8y = 16

y = 16 / 8

Divide the terms

y = 2

Substitute the value of x in the first equation

4x + 3y = 10

4x + 3×2 = 10

Multiply the terms

4x + 6 = 10

4x = 10 - 6

4x = 4

x = 4 / 4

Divide the terms

x = 1

Hence, the solutions of the equations are x = 1 and y = 2

Learn more about elimination method here

brainly.com/question/14619835

#SPJ1

7 0

1 year ago

Jacob works as a mechanic at an hourly rate of $36 and earns time and a half for for any overtime. Last week he worked 37 hours

Korvikt [17]

Answer:

1620 which isn't there so I'm probably wrong but maybe c or a

Step-by-step explanation:

all we do is 36(37+8) and first we do 37 plus 8 that's 45 so 45×36

4 0

3 years ago

Christine sleep form 11pm until 9am what fraction of a day does Christine sleep​

Christine sleep form 11pm until 9am what fraction of a day does Christine sleep