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(3x^2+c_{1)},y=-2x-sqrt(3x^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 + 3 x^{2} + c_{1}, y = - 2 x - 3 x^{2} + c_{1}

Solution steps

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

Solve exact ODE:

y = - 2 x + 3 x^{2} + c_{1}, y = - 2 x - 3 x^{2} + c_{1}

y = - 2 x + 3 x^{2} + c_{1}, y = - 2 x - 3 x^{2} + c_{1}

\int (x^{2} + 3)^{5} d x

\int 42 sec^{4} (x) d x

x^{2}, 0, 2

\int x \frac{1}{1 - x ^{2}} d x

\frac{d}{d x} (10 cos^{3} (x))

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(3x^2+c_{1)},y=-2x-sqrt(3x^2+c_{1)}