Mathematics: How that every member of the family of functions y = (4 ln(x) + c)/x is a solution of the differential equation x2y + xy = 4. (simplify as much as possible.)

Hello There!In scientific notation, this would be 9.66 x Move the decimal place four places to the left so you will get a number between 1 and 10....

How that every member of the family of functions

030702princessjs

12.01.2022

$y=\dfrac{4\ln x+C}x\implies y'=\dfrac{x(4\ln x+C)'-(4\ln x+C)(x)'}{x^2}=\dfrac{4-4\ln x-C}{x^2}$

Substitute this into the differential equation:

$x^2y'+xy=4-4\ln x-C+4\ln x+C=4$

so every solution of the given form is a solution.

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bookprincesslol

13.04.2022

Hello There!

In scientific notation, this would be 9.66 x $10^{4}$

Move the decimal place four places to the left so you will get a number between 1 and 10.

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