Linear Differential Equation in Strange Form

[Gooolati]

Homework Statement

ydx - 4(x + y^6)dy = 0

Homework Equations

Need to get into the form of dy$$/dx$$ + f(x)y = G(x)
(Standard Form)

The Attempt at a Solution

ydx = 4(x + y^6)dy

y = 4(x + y^6) dy/dx

y$$/4(x + y^6)$$ = dy/dx

then I don't know how to get it in the Standard form
All help is appreciated, thanks!

 

[HallsofIvy]

You can't. That's not a linear equation to begin with ([itex]y^6[/tex] is not linear) and you can't just force it into "standard form" for a linear equation.[/itex]

 

[Gooolati]

Oh I can see that now! I just wonder why it's in the Linear Equations section haha.

 

[sagardip]

See , sometimes in order to solve problems of this sort, we treat y as the independent variable and x as the dependent variable and convert it into a linear equation in the variable x.So now in place of dy/dx we have dx/dy and then we solve it using the integrating factor which in this case is 1/y.

 

[pr0blumz]

Try dx/dy -4/y*x = 4y^6