What is the solution for e^{-(x^2+y^2)}(xdx+ydy)=0 ?

The solution for e^{-(x^2+y^2)}(xdx+ydy)=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}

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e^{-(x^2+y^2)}(xdx+ydy)=0

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

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

Solution steps

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

Solve separable ODE:

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

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

x^{2} y d y - e^{y} d x = 0

y^{^{'}} = \frac{y + 3}{7 t + 50}, y (2) = 0

(2 x - 8 x y) d x - (x^{2} + 4) d y = 0

\frac{y}{x} \frac{d y}{d x} = (1 + x^{2}) (1 + y^{2})

y - x y^{^{'}} = 1 + x^{2} y^{^{'}}

What is the solution for e^{-(x^2+y^2)}(xdx+ydy)=0 ?
The solution for e^{-(x^2+y^2)}(xdx+ydy)=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}