How to Solve a Non-Separable Differential Equation?

[hotjohn]

Homework Statement

i was given dy/dx = -(4x+4y) / (4x+4y-2) , v= x +y . I have tried to do ( as in the photo) , but I didn't get the ans , in the last line of my working , the V and x are not separable , which part of my working is wrong ?

Homework Equations

The Attempt at a Solution

 

[phyzguy]

If v = x+y, then dv/dx = 1 + dy/dx, not x + dy/dx as you wrote.

 

[hotjohn]

If v = x+y, then dv/dx = 1 + dy/dx, not x + dy/dx as you wrote.

i have redone the question , but i gt stucked here , how to proceed?

btw , the ans given is - ( (x+y) ^2 ) +(x+y ) = x +A

 

[phyzguy]

Check your signs again.

 

[hotjohn]

Check your signs again.

ok , i gt it correct now , thanks