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

The solution for 4x^2(dy)/(dx)=(dy)/(dx)+4xe^{-y} is y=ln(1/2 ln(4x^2-1)+c_{1})

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4x^2(dy)/(dx)=(dy)/(dx)+4xe^{-y}

4 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 4 x e^{- y}

y = ln (\frac{1}{2} ln (4 x^{2} - 1) + c_{1})

Solution steps

4 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 4 x e^{- y}

Solve separable ODE:

y = ln (\frac{1}{2} ln (4 x^{2} - 1) + c_{1})

y = ln (\frac{1}{2} ln (4 x^{2} - 1) + c_{1})

\int_{0}^{1} π (y - y^{4}) d y

\int \frac{4 x + 6}{( x ^{2} + 3 x + 7 ) ^{3}} d x

\frac{x ^{5}}{8}

\frac{10}{s}

x \to \infty lim (1.0 2^{x})

What is the solution for 4x^2(dy)/(dx)=(dy)/(dx)+4xe^{-y} ?
The solution for 4x^2(dy)/(dx)=(dy)/(dx)+4xe^{-y} is y=ln(1/2 ln(4x^2-1)+c_{1})