What is the solution for (4e^{2x}+2xy-y^2)dx+(x-y)^2dy=0 ?

The solution for (4e^{2x}+2xy-y^2)dx+(x-y)^2dy=0 is y=-\sqrt[3]{-c_{1}+6e^{2x}+x^3}+x

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(4e^{2x}+2xy-y^2)dx+(x-y)^2dy=0

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

y = - 3 - c_{1} + 6 e^{2 x} + x^{3} + x

Solution steps

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

Solve exact ODE:

y = - 3 - c_{1} + 6 e^{2 x} + x^{3} + x

y = - 3 - c_{1} + 6 e^{2 x} + x^{3} + x

2 e^{- 2 t}

f (x) = arctan (x^{3})

\int \frac{1}{3 u} d u

\int \frac{- 6}{x} d x

4 x^{2} (3 x^{3} - 2 x^{2} + 5 x)

What is the solution for (4e^{2x}+2xy-y^2)dx+(x-y)^2dy=0 ?
The solution for (4e^{2x}+2xy-y^2)dx+(x-y)^2dy=0 is y=-\sqrt[3]{-c_{1}+6e^{2x}+x^3}+x