What is the solution for 1/8 (dy)/(dx)=ysqrt(4x^2-1) ?

The solution for 1/8 (dy)/(dx)=ysqrt(4x^2-1) is y=(e^{4xsqrt(4x^2-1)+c_{1}})/(8x^2+4xsqrt(4x^2-1)-1)

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1/8 (dy)/(dx)=ysqrt(4x^2-1)

\frac{1}{8} \frac{d y}{d x} = y 4 x^{2} - 1

y = \frac{e ^{4 x 4 x^{2} - 1 + c_{1}}}{8 x ^{2} + 4 x 4 x ^{2} - 1 - 1}

Solution steps

\frac{1}{8} \frac{d y}{d x} = y 4 x^{2} - 1

Solve separable ODE:

y = \frac{e ^{4 x 4 x^{2} - 1 + c_{1}}}{8 x ^{2} + 4 x 4 x ^{2} - 1 - 1}

y = \frac{e ^{4 x 4 x^{2} - 1 + c_{1}}}{8 x ^{2} + 4 x 4 x ^{2} - 1 - 1}

\frac{y ^{^{'}}}{x} = - y

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

\frac{d y}{d x} = 3 y, y (0) = 5

y^{^{'}} - k y = 180

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

What is the solution for 1/8 (dy)/(dx)=ysqrt(4x^2-1) ?
The solution for 1/8 (dy)/(dx)=ysqrt(4x^2-1) is y=(e^{4xsqrt(4x^2-1)+c_{1}})/(8x^2+4xsqrt(4x^2-1)-1)