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}

f (x) = \frac{x}{x ^{2} - 5}

x \to - 1 lim (\frac{x ^{3} + 1}{x + 1})

f (x) = \frac{4}{3 x - 1}, at x = 3

ln (4 x^{3} + 5 x^{2} + 2 x + 5)

\int \frac{( x ^{2} - 64 )}{x} d x

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