What is the solution for 2(dy)/(dx)=(xe^{-y})/(sqrt(x^2+3)) ?

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

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2(dy)/(dx)=(xe^{-y})/(sqrt(x^2+3))

2 \frac{d y}{d x} = \frac{x e ^{- y}}{x ^{2} + 3}

y = ln (\frac{x ^{2} + 3}{2} + c_{1})

Solution steps

2 \frac{d y}{d x} = \frac{x e ^{- y}}{x ^{2} + 3}

Solve separable ODE:

y = ln (\frac{x ^{2} + 3}{2} + c_{1})

y = ln (\frac{x ^{2} + 3}{2} + c_{1})

t^{2} (1 + y^{2}) + 2 y \frac{d y}{d t} = 0

\frac{d P}{d t} = 0.05 P - 0.00125 P (t)^{2}

y e^{3 x} d x = (9 - e^{3 x}) d y

y y^{^{'}} - 3 x^{2} - x = 0

e^{x} cos (y) d x + (1 + e^{x}) sin (y) d y = 0

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