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Mathematics

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AlexFokin [52]2 years ago

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Which of the following is a solution to the differential equation xy′−3y=6 ?

ololo11 [35]

Answer:

$y = 5 {x}^{3} - 2$

Step-by-step explanation:

The given differential equation is :

xy′−3y=6

We want to determine which of the following options is a solution to the differential equations.

The function that satisfies the differential equation is a solution.

We can verify that

$y = 5 {x}^{3} - 2$

satisfy this differential equation.

We differentiate to get:

$y' = 15 {x}^{2}$

We substitute the function and its derivative into the differential equation to get:

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We expand and simplify on the left:

$15 {x}^{3}- 15 {x}^{3} + 6= 6$

This simplifies to:

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Verified.

We can show that all the other functions do not satisfy this differential equation

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