Not sure what to do with this DE problem

  • Thread starter iRaid
  • Start date
  • #1
559
8

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? :confused:
 

Answers and Replies

  • #2
pasmith
Homework Helper
1,964
599

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? :confused:
It means substitute [itex]y = x^3 + 7[/itex] into [itex]y' = 3x^2[/itex] to get [itex](x^3 + 7)' = 3x^2[/itex] 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 [itex](x^3 + 7)' = (x^3)' + (7)' = 3x^2 + 0 = 3x^2[/itex].
 
  • #3
559
8
Why do they make me even do this...?
 
  • #4
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,668
Usually, they don't anticipate the student having any problem verifying an equation given its solution.
 

Related Threads on Not sure what to do with this DE problem

Replies
2
Views
4K
Replies
1
Views
969
Replies
3
Views
1K
Replies
14
Views
2K
Replies
9
Views
772
Replies
4
Views
932
Replies
6
Views
1K
  • Last Post
Replies
7
Views
856
  • Last Post
Replies
4
Views
3K
Top