What is the solution for ydx+x^{α/6}dy=8yxdx+2dy ?

The solution for ydx+x^{α/6}dy=8yxdx+2dy is y=e^{integral of (8x-1)/(x^{α/6)-2}}

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ydx+x^{α/6}dy=8yxdx+2dy

y d x + x^{\frac{α}{6}} d y = 8 y x d x + 2 d y

y = e^{\int \frac{8 x - 1}{x ^{\frac{α}{6}} - 2} d x}

Solution steps

y d x + x^{\frac{α}{6}} d y = 8 y x d x + 2 d y

Solve separable ODE:

y = e^{\int \frac{8 x - 1}{x ^{\frac{α}{6}} - 2} d x}

y = e^{\int \frac{8 x - 1}{x ^{\frac{α}{6}} - 2} d x}

\frac{d}{d x} (2 x^{6} + 3 x^{5} + 4 x^{4} - 5 x^{3} - 6 x^{2} + 1)

ln (x^{2} + 1)

- 6 t (5 t^{3} - 1)^{7}

x \to - 3 lim (x^{2} - 5)

x \to 2 - lim (\frac{2 x}{x - 2})

What is the solution for ydx+x^{α/6}dy=8yxdx+2dy ?
The solution for ydx+x^{α/6}dy=8yxdx+2dy is y=e^{integral of (8x-1)/(x^{α/6)-2}}