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}

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)}