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3 years ago

Expression

1 answer:

4 0

The value of the expression is -24

This is because you distribute the -4 to both of the values in the parenthesis like this:
-4(7) + -4(-1)
This can be simplified to:
-28 + 4
Which equals -24
Hope this helps!

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Step-by-step explanation:

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Match solutions and differential equations. Note: Each equation may have more than one solution. Select all that apply. (a) 7y''

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Answer:

a- $e^x,e^{-x}$

b- $x^{-2}$

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Step-by-step explanation:

a.7 y''-7 y =0

Auxillary equation

$D^2-1=0$

$(D-1)(D+1)=0$

D=1,-1

Then , the solution of given differential equation

$y=e^x,y=e^{-x}$

2. $7x^2y''+14xy'-14 y=0$

Y= $y=x^3$

$y=3x^2$

$y''=6x$

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$42x^3+42x^3-14x^3\neq 0$

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$e^x,e^{-x}$ are also not a solution of given differential equation.

y= $x^{-2}$

$y'=-2x^{-3}$

$y''=6x^{-4}$

Substitute the values in the differential equation

$7x^2(6x^{-4})+14x(-2x^{-3})-14 x^{-2}$

= $42x^{-2}-28x^{-2}-14x^{-2}=0$

Hence, $x^{-2}$ is a solution of given differential equation.

c. $7x^2y''-42y=0$

$y=x^3$

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$y''=6x$

Substitute the values in the differential equation

$42x^3-42x^3=0$

Hence, $x^3$ is a solution of given differential equation.

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b- $x^{-2}$

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