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the question is given in the attachment in case the attachment is not appearing i have mentioned this question: Solve the differential equation yexydx=⎛⎜⎝xexy+y2⎞⎟⎠ dy. (toppr.com) in this question they have solved the differential equation by substituting v = x/y, but as of my knowledge, this substitution can be made only for zero order homogeneous differential equations, yet the answer they got is correct and is verified by calculator, so does this mean that we can appl this substitution to any differential equation? PS: in some sites they have solved this question by other methods and they have specified substituting v = x/y wont work here as this is not a homogenous differential equation. So can you clarify what is the correct way to solve this question, THANK YOU!
Asked by ashwinskrishna2006 | 24 Dec, 2023, 04:59: PM

You can solve the given differential equation using the substitution  v = x/y .

The question of homogeneous equation does not arise because the substitution ' y = v x ' is

used in homogeneous type of equation , where as here  y = x/v is used

( expression of dy/dx differs in both the case )

Since you are aware of the method of solving this differential equation , I have not solved it

Answered by Thiyagarajan K | 25 Dec, 2023, 12:00: PM

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