Differential Equation solve differential equation (dy)/( dx) =((3x-y-6))/((x+y+2)) I tried to do this but it´s first order and posible is separable variables

Rubi Garner 2022-10-22 Answered
Differential Equation
solve differential equation
d y d x = ( 3 x y 6 ) ( x + y + 2 )
I tried to do this but it´s first order and posible is separable variables
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Answers (1)

silenthunter440
Answered 2022-10-23 Author has 19 answers
From d y d x = ( 3 x y 6 ) ( x + y + 2 ) , we have
( x + y + 2 ) d y ( 3 x y 6 ) d x = 0
We look for F ( x , y ) such that
F y = x + y + 2
F y = x + y + 2
F x = ( 3 x y 6 )
Solve for F, F ( x , y ) = x y + y 2 2 + 2 y 3 x 2 2 + 6 x
The solution is F(x,y) = Constant.
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