Not sure what to do with this DE problem

1. Sep 8, 2013

iRaid

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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?

2. Sep 8, 2013

pasmith

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 $(x^3 + 7)' = (x^3)' + (7)' = 3x^2 + 0 = 3x^2$.

3. Sep 8, 2013

iRaid

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

4. Sep 8, 2013

SteamKing

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