What is the solution for (2x+y)dx+(x+3y)dy=0 ?

The solution for (2x+y)dx+(x+3y)dy=0 is y=(-x+sqrt(-5x^2+c_{1)})/3 ,y=-(x+sqrt(-5x^2+c_{1)})/3

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(2x+y)dx+(x+3y)dy=0

(2 x + y) d x + (x + 3 y) d y = 0

y = \frac{- x + - 5 x ^{2} + c _{1}}{3}, y = - \frac{x + - 5 x ^{2} + c _{1}}{3}

Solution steps

(2 x + y) d x + (x + 3 y) d y = 0

Solve exact ODE:

y = \frac{- x + - 5 x ^{2} + c _{1}}{3}, y = - \frac{x + - 5 x ^{2} + c _{1}}{3}

y = \frac{- x + - 5 x ^{2} + c _{1}}{3}, y = - \frac{x + - 5 x ^{2} + c _{1}}{3}

y = 4 x^{2} - x^{3}, (1, 3)

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\frac{\partial}{\partial x} (8 - 3 x^{2} - y^{2})

\int \frac{x ^{2} + 2 x - 6}{x ^{3} - x} d x

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What is the solution for (2x+y)dx+(x+3y)dy=0 ?
The solution for (2x+y)dx+(x+3y)dy=0 is y=(-x+sqrt(-5x^2+c_{1)})/3 ,y=-(x+sqrt(-5x^2+c_{1)})/3