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

The solution for 1/(8x)(dy)/(dx)=ysqrt(4x^2-1) is y=e^{2/3 (4x^2-1)^{3/2}+c_{1}}

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

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

y = e^{\frac{2}{3} (4 x^{2} - 1)^{\frac{3}{2}} + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{\frac{2}{3} (4 x^{2} - 1)^{\frac{3}{2}} + c_{1}}

y = e^{\frac{2}{3} (4 x^{2} - 1)^{\frac{3}{2}} + c_{1}}

What is the solution for 1/(8x)(dy)/(dx)=ysqrt(4x^2-1) ?
The solution for 1/(8x)(dy)/(dx)=ysqrt(4x^2-1) is y=e^{2/3 (4x^2-1)^{3/2}+c_{1}}