Is this equation solvable and if so, how?

  • Context: Undergrad 
  • Thread starter Thread starter MecEngStudent
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Discussion Overview

The discussion centers around the solvability of a differential equation presented in the form xy' = 3y + (cosx)x^4. Participants explore methods to solve the equation and express differing views on its nature and solvability.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about solving the equation, noting it is non-separable.
  • Another participant reformulates the equation into a different form, suggesting a method involving differentiation and arriving at a solution y = (sinx)x^3.
  • A third participant reiterates the complexity of differential equations beyond just separable ones, implying that there are various methods to consider.
  • A later reply builds on the previous reformulation, introducing an arbitrary constant C and presenting a general solution y = (sinx + C)x^3.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the approach to solving the equation, with some expressing confusion and others proposing solutions that may or may not be universally accepted.

Contextual Notes

There is an indication of differing levels of understanding regarding the methods applicable to differential equations, and the discussion does not resolve the initial confusion about the equation's solvability.

MecEngStudent
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xy'=3y+(cosx)x^4

I don't understand how to solve it since it's non-separable.
 
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y'/x^3-3y/x^4=cosx

d/dx(y/x^3)=cosx

y/x^3=sinx

y=(sinx)x^3
 
MecEngStudent said:
I don't understand how to solve it since it's non-separable.

There's more to Differential Equations than just the separable ones. A LOT more.
 
Surely

d/dx(y/x^3)=cosx

y/x^3=sinx+C

y=(sinx+C)x^3

where C is an arbitrary constant.
 

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