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

The solution for (2x+y)dx+(x-2y)dy=0 is y=-(-x+sqrt(5x^2-c_{1)})/2 ,y=-(-x-sqrt(5x^2-c_{1)})/2

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(2x+y)dx+(x-2y)dy=0

(2 x + y) d x + (x - 2 y) d y = 0

y = - \frac{- x + 5 x ^{2} - c _{1}}{2}, y = - \frac{- x - 5 x ^{2} - c _{1}}{2}

Solution steps

(2 x + y) d x + (x - 2 y) d y = 0

Solve exact ODE:

y = - \frac{- x + 5 x ^{2} - c _{1}}{2}, y = - \frac{- x - 5 x ^{2} - c _{1}}{2}

y = - \frac{- x + 5 x ^{2} - c _{1}}{2}, y = - \frac{- x - 5 x ^{2} - c _{1}}{2}

f (x) = 4 x^{2} ln (4 x)

\frac{d}{d x} (2 x - 5 y + 3)

\frac{d y}{d x} = e^{6 x + 5 y}

\frac{d}{d x} (\frac{x ^{5}}{1 - x ^{4}})

\frac{d}{d x} ((x^{2} + 2)^{3})

What is the solution for (2x+y)dx+(x-2y)dy=0 ?
The solution for (2x+y)dx+(x-2y)dy=0 is y=-(-x+sqrt(5x^2-c_{1)})/2 ,y=-(-x-sqrt(5x^2-c_{1)})/2