Solving DE: Integrating Factor Method

[gbacsf]

What approach should be used to solve the following DE:

dy/dx= (-2x+5y)/(2x+y)

Find an integrating factor and solve it as an excact equation?

Thanks.

 

[Tide]

See what happens if you define a new variable: z = y/x

 

[gbacsf]

Thanks!

Right, I get

1/[(-2+5z)/(2+z)-z] dz = (1/x) dx

so

3ln(z-1) -4ln(z-2) = lnx +c

and

3ln(y/x -1) -4ln(y/x-2)-lnx = c

?

 

[Tide]

Good - but I got different signs on my first try. You should recheck.