What is the solution for (x+y)dx+(x+y-4)dy=0 ?

The solution for (x+y)dx+(x+y-4)dy=0 is y=(8-2x+sqrt(64-32x+c_{1)})/2 ,y=(8-2x-sqrt(64-32x+c_{1)})/2

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(x+y)dx+(x+y-4)dy=0

(x + y) d x + (x + y - 4) d y = 0

y = \frac{8 - 2 x + 64 - 32 x + c _{1}}{2}, y = \frac{8 - 2 x - 64 - 32 x + c _{1}}{2}

Solution steps

(x + y) d x + (x + y - 4) d y = 0

Solve exact ODE:

y = \frac{8 - 2 x + 64 - 32 x + c _{1}}{2}, y = \frac{8 - 2 x - 64 - 32 x + c _{1}}{2}

y = \frac{8 - 2 x + 64 - 32 x + c _{1}}{2}, y = \frac{8 - 2 x - 64 - 32 x + c _{1}}{2}

What is the solution for (x+y)dx+(x+y-4)dy=0 ?
The solution for (x+y)dx+(x+y-4)dy=0 is y=(8-2x+sqrt(64-32x+c_{1)})/2 ,y=(8-2x-sqrt(64-32x+c_{1)})/2