Question

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

Answer 1

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:

$x(15 {x}^{2}) - 3(5 {x}^{3} - 2) = 6$

We expand and simplify on the left:

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

This simplifies to:

$6 = 6$

Verified.

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