Question

Determine which function is a solution to the differential equation xy ' + 2y = 0.

e^2x
x^2
x^-2
None of these

Thus far, I have ruled out option a.

Thank you!

Answer 1

Answer:

x⁻²

Step-by-step explanation:

If y = e²ˣ, y' = 2e²ˣ.

2xe²ˣ + 2e²ˣ ≠ 0

If y = x², y' = 2x.

2x² + 2x² ≠ 0

If y = x⁻², y' = -2x⁻³.

-2x⁻² + 2x⁻² = 0

Answer 2

The x^-2 function is a solution to the differential equation

$xy ' + 2y = 0.$

We have given,

The differential equation$xy ' + 2y = 0.$

What is the differential equation?

A differential equation is an equation with one or more derivatives of a function. The derivative of the function is given by dy/dx.

If $y = e^{2x}, y' = 2e^{2x}.$

$2xe^2x + 2e^2x$≠0

If $y = x^2, y' = 2x.$

$2x^2 + 2x^2$≠0

If$y = x^-2, y' = -2x^-3.$

$-2x^-2 + 2x^-2= 0$

Therefore, the x^-2 function is a solution to the differential equation

$xy ' + 2y = 0.$

To learn more about the differential equation visit:

https://brainly.com/question/1164377

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