Not sure what to do with this DE problem

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Homework Help Overview

The discussion revolves around verifying a given function as a solution to a differential equation, specifically focusing on the function y = x^3 + 7 and its derivative y' = 3x^2.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the process of verification by substitution and question the necessity of this task. Some express confusion about what is meant by verifying through substitution.

Discussion Status

There is an ongoing exploration of the verification process, with some participants providing explanations about substituting the function into the differential equation. However, there is no clear consensus on the value of the exercise itself.

Contextual Notes

Participants express frustration regarding the assignment, suggesting that it may not be expected for students to struggle with such verification tasks.

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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:
 
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iRaid said:

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].
 
Why do they make me even do this...?
 
Usually, they don't anticipate the student having any problem verifying an equation given its solution.
 

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