Not sure what to do with this DE problem

[iRaid]

Homework Statement

Verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with respect to x.
y'=3x²; y=x³+7

Homework Equations

The Attempt at a Solution

Well obviously I see that the derivative of y=x³+7 is just 3x², but what does it mean by verifying by substitution?

 

[pasmith]

Homework Statement

Verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with respect to x.
y'=3x²; y=x³+7

Homework Equations

The Attempt at a Solution

Well obviously I see that the derivative of y=x³+7 is just 3x², but what does it mean by verifying by substitution?

It means substitute $y = x^3 + 7$ into $y' = 3x^2$ to get $(x^3 + 7)' = 3x^2$ and then confirm that the left hand side does in fact equal the right hand side. In this case it obviously does, so there's nothing more to do. Although I suppose you could expressly state that $(x^3 + 7)' = (x^3)' + (7)' = 3x^2 + 0 = 3x^2$.

 

[iRaid]

Why do they make me even do this...?

 

[SteamKing]

Usually, they don't anticipate the student having any problem verifying an equation given its solution.