Question

Find the general solution for the following differential equation: y' + 8y = -6y^-8
What substitution will you make?

Answer 1

@Loser66

Answer 2

@wio

Answer 3

I don't see any substitution needed there, just y' = \(\dfrac {-6}{y^8}-8y= -\dfrac{6+8y^9}{y^8}\) then
\[\frac{dy}{dx}=-\frac{6+y^9}{y^8}\rightarrow \frac{y^8}{6+y^9}dy=-dx\]
integral both sides, that's it

Answer 4

thats what i got but its online and its asking for a sub

Answer 5

the sub is v(t) =y^9 only thing i cant get is the general solution

Answer 6

This looks like a Bernoulli equation, which would explain the choice of substitution.