I Dont Understand can someone please help me and explain

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

3 years ago

Find the product of two numbers before multiplying by the next number. 25 × 3 × 2

Varvara68 [4.7K]

Answer and explanation:

25 x 3 = 75

75 x 2 = 150

I found the product of the first two numbers, then multiplied the third.

The answer is 150. Hope this helps!

5 0

4 years ago

What is the height of an equilateral triangle with side lengths of 14?

olganol [36]

If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.
If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.

5 0

4 years ago

Read 2 more answers

Find the distance between each pair of points 8) (2, 6), (5, 10) 9) (-3,-10), (-3,5)

Lapatulllka [165]

Answer:

8) answer=5 9)answer=15

Step-by-step explanation:

all you have to do is replace in the following formula

$\sqrt{(x2-x1)^{2}+ (y2-y1)^{2}} =d$

Where

X1: is the first number of the first point

Y1: is the second number of the first point

X2: is the first number of the second point

Y2: is the second number of the second point

you replace in the formula and solve

I attach solution

4 0

3 years ago

Renee is sewing a quilt whose pattern contains right triangles.

Mashutka [201]

Answer:

8 inches

Step-by-step explanation:

The area of a triangle is ...

A = 1/2bh

Filling in the given values, we have ...

24 = 1/2b(6)

24/3 = b = 8 . . . . . divide by the coefficient of b

The base of each triangular quilt piece is 8 inches long.

7 0

3 years ago