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

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

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

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

y = 2 x - 5 x^{2} - c_{1}, y = 2 x + 5 x^{2} - c_{1}

Solution steps

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

Solve exact ODE:

y = 2 x - 5 x^{2} - c_{1}, y = 2 x + 5 x^{2} - c_{1}

y = 2 x - 5 x^{2} - c_{1}, y = 2 x + 5 x^{2} - c_{1}

y^{^{''}} - 3 y^{^{'}} + 2 y = 0

x + y y^{^{'}} = 0

\frac{d y}{d x} = \frac{( e ^{x} )}{y ^{2}}

\int \frac{1}{p ^{2} + 1} d p

\frac{d}{d x} (x e^{y} + y^{2} e^{x} - \frac{1}{3} x + 4)

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