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Homogeneous ODE Help

So I managed to get to dV/dX=(1/x)*((v^(4)+1)/(v^5)

I used y=vx as subsitution but, I am unsure on how to proceed I know your meant to just separate the variables and integrate them but,I am unsure on how to do that. Also, I need to change V to Y and X at the end.

Can someone guide me on how to do this
(edited 1 year ago)
Original post by Summerx678
So I managed to get to dV/dX=(1/x)*((v^(4)+1)/(v^5)

I used y=vx as subsitution but, I am unsure on how to proceed I know your meant to just separate the variables and integrate them but,I am unsure on how to do that. Also, I need to change V to Y and X at the end.

Can someone guide me on how to do this

With seperation of varibles you have something like
dv/dx = f(v)g(x)
so
Int 1/f(v) dv = Int g(x) dx
So start with that and see how you go.

It would help to see the original question / your current working to see what substitution youre referring to, but you can solve the ode youve posted in terms of v and x.
(edited 1 year ago)

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