What is the solution for y(6y^2-x-1)dx+2xdy=0 ?

The solution for y(6y^2-x-1)dx+2xdy=0 is y=sqrt((xe^x)/(6e^x+c_{1))},y=-sqrt((xe^x)/(6e^x+c_{1))}

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y(6y^2-x-1)dx+2xdy=0

y (6 y^{2} - x - 1) d x + 2 x d y = 0

y = \frac{x e ^{x}}{6 e ^{x} + c _{1}}, y = - \frac{x e ^{x}}{6 e ^{x} + c _{1}}

Solution steps

y (6 y^{2} - x - 1) d x + 2 x d y = 0

Solve Bernoulli ODE:

y = \frac{x e ^{x}}{6 e ^{x} + c _{1}}, y = - \frac{x e ^{x}}{6 e ^{x} + c _{1}}

y = \frac{x e ^{x}}{6 e ^{x} + c _{1}}, y = - \frac{x e ^{x}}{6 e ^{x} + c _{1}}

What is the solution for y(6y^2-x-1)dx+2xdy=0 ?
The solution for y(6y^2-x-1)dx+2xdy=0 is y=sqrt((xe^x)/(6e^x+c_{1))},y=-sqrt((xe^x)/(6e^x+c_{1))}