What is the solution for (2x+8y)dx+(8x+4y)dy=0 ?

The solution for (2x+8y)dx+(8x+4y)dy=0 is y=(-8x+sqrt(56x^2+c_{1)})/4 ,y=(-8x-sqrt(56x^2+c_{1)})/4

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(2x+8y)dx+(8x+4y)dy=0

(2 x + 8 y) d x + (8 x + 4 y) d y = 0

y = \frac{- 8 x + 56 x ^{2} + c _{1}}{4}, y = \frac{- 8 x - 56 x ^{2} + c _{1}}{4}

Solution steps

(2 x + 8 y) d x + (8 x + 4 y) d y = 0

Solve exact ODE:

y = \frac{- 8 x + 56 x ^{2} + c _{1}}{4}, y = \frac{- 8 x - 56 x ^{2} + c _{1}}{4}

y = \frac{- 8 x + 56 x ^{2} + c _{1}}{4}, y = \frac{- 8 x - 56 x ^{2} + c _{1}}{4}

What is the solution for (2x+8y)dx+(8x+4y)dy=0 ?
The solution for (2x+8y)dx+(8x+4y)dy=0 is y=(-8x+sqrt(56x^2+c_{1)})/4 ,y=(-8x-sqrt(56x^2+c_{1)})/4