Helping on how to do find solution to diff equation

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  • Thread starter Thread starter Pepsi24chevy
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Discussion Overview

The discussion revolves around solving a differential equation by finding the values of k for which the function y = x^2 + k is a solution to the equation 2y - xy' = 10. Participants are exploring the setup and steps needed to approach this problem, including the differentiation of the function and substitution into the equation.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to set up the problem and whether to keep taking derivatives of the differential equation.
  • Another participant outlines a step-by-step approach, suggesting to compute y', substitute y and y' into the differential equation, and solve for k.
  • A participant calculates the derivative y' as 2x + 1 and attempts to substitute this into the differential equation but remains uncertain about how to determine k and questions if the derivative of the constant k is 1.
  • Another participant clarifies that the derivative of a constant is 0.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the method for determining k, and there is uncertainty regarding the treatment of the constant k in differentiation.

Contextual Notes

The discussion includes assumptions about the differentiation process and the nature of constants in calculus, which may not be fully resolved.

Pepsi24chevy
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Hey guys, the problem reads: Find the values of k for which y=x^2+k i sa solution to the differenital equation: 2y-xy`= 10. Anyways I am confused on how to set this up. DO i keep taking the derivative of the dif equation and plugging is back into the first one or what. :redface:
 
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1) Compute y' from your given expression for y(x)
2) Insert the given expressions for y and y' into the expression making the left-hand side of the differential equation.
3) Determine the value(s) of "k" so that what you got in 2) equals 10.
 
Thanks. So i got y`= 2x+1 so then i plug then info i have into the differential equation so that i get 2(x^2+1) - x(2x+1) = 10. Now i am still not quit sure how to determine K. Also is the deriviative of the K constant 1?
 
the derivative of a constant is 0
 

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