Question

how to solve \[2(2xy + 4y -3)dx + (x+2)^2 dy = 0\] via the Integrating Factor Method (Linear Differential Equations)

Answer 1

@dpaInc

Answer 2

@Zarkon

Answer 3

@satellite73

Answer 4

@turingtest

Answer 5

2( 2xy + 4y −3 )dx + (x+2)² dy = 0
-> dy/dx = - 4y/(x +2) + 6/ (x+2)²
4y/(x +2) + dy/dx = 6/ (x+2)²

Let I = e^ 4∫ dx/(x +2) = e^ [ ln (x+2)^4 ] = ( x+2) ^4
=> ( x+2) ^4* y = 6 ∫ ( x+2) ^4 dx/ (x+2)²
= 6 ∫ (x+2)² dx

Answer 6

Can you continue from here?