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

The solution for (2xy+x)dx+(x^2+y)dy=0 is y=-x^2+sqrt(x^4-x^2+c_{1)},y=-x^2-sqrt(x^4-x^2+c_{1)}

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(2xy+x)dx+(x^2+y)dy=0

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

y = - x^{2} + x^{4} - x^{2} + c_{1}, y = - x^{2} - x^{4} - x^{2} + c_{1}

Solution steps

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

Solve exact ODE:

y = - x^{2} + x^{4} - x^{2} + c_{1}, y = - x^{2} - x^{4} - x^{2} + c_{1}

y = - x^{2} + x^{4} - x^{2} + c_{1}, y = - x^{2} - x^{4} - x^{2} + c_{1}

\int 9.8 x d x

\frac{\partial}{\partial t} (0)

\int - 4 x^{\frac{3}{2}} + 3 x^{\frac{2}{3}} - 4 x^{2} d x

\int \frac{2}{x 4 - ( ln ( x ) ) ^{2}} d x

y^{^{''}} - 8 y^{^{'}} + 12 y = 0

What is the solution for (2xy+x)dx+(x^2+y)dy=0 ?
The solution for (2xy+x)dx+(x^2+y)dy=0 is y=-x^2+sqrt(x^4-x^2+c_{1)},y=-x^2-sqrt(x^4-x^2+c_{1)}