Which of the following is a solution to the differential equation xy′−3y=6 ?
y=x^2+2
y=3x^2−2
y=5x^3−2
y=7x^3+2

The solution of the given differential equation is .

Given information:

The differential equation is .

It is required to find the solution of the differential equation.

So, rearrange the differential equation as,

By analysis, we can say that the equation is the solution of the given differential equation because it satisfies the differential equation.

Check for the solution as,

Hence proved.

Therefore, the solution of the given differential equation is .

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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

satisfy this differential equation.

We differentiate to get:

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

We expand and simplify on the left:

This simplifies to:

Verified.

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

hard

step-by-step explanation: