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sleet_krkn [62]

3 years ago

11

Solve for x. 2 ( x + 1 ) = 12

2 answers:

MAVERICK [17]3 years ago

8 0

Answer:

Use the distributive property and you get 5.

2(x+1) = 12

2x + 2 = 12

Subtract 2 from both sides

2x = 10

Solve x.

x = 5

Evgen [1.6K]3 years ago

5 0

2 ( x + 1 ) = 12

Use distributive property:

2x + 2 = 12

Subtract 2 from both sides:

2x = 10

Divide both sides by 2:

X = 5

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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

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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

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

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$\Rightarrow m = 3, -\frac13$

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

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

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(I think that's what that says)

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Go from left to right

-7 - 8 = -15

-15 - (-8) = -7

-7 - 14 = -21

-21 - 30 = -51

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