What is the solution for (x-1)dy+(y-x^2+2x^{-3})dx=0 ?

The solution for (x-1)dy+(y-x^2+2x^{-3})dx=0 is y=(x^3)/(3(x-1))+1/(x^2(x-1))+(c_{1})/(x-1)

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(x-1)dy+(y-x^2+2x^{-3})dx=0

(x - 1) d y + (y - x^{2} + 2 x^{- 3}) d x = 0

y = \frac{x ^{3}}{3 ( x - 1 )} + \frac{1}{x ^{2} ( x - 1 )} + \frac{c _{1}}{x - 1}

Solution steps

(x - 1) d y + (y - x^{2} + 2 x^{- 3}) d x = 0

Solve linear ODE:

y = \frac{x ^{3}}{3 ( x - 1 )} + \frac{1}{x ^{2} ( x - 1 )} + \frac{c _{1}}{x - 1}

y = \frac{x ^{3}}{3 ( x - 1 )} + \frac{1}{x ^{2} ( x - 1 )} + \frac{c _{1}}{x - 1}

x = y^{\frac{1}{2}}, x = 2 [0, 2]

f (x) = x^{2}, at x = 0.2

f (x) = \frac{7}{x ^{2}}

\int \frac{1}{3} sec (x) tan (x) d x

\frac{d}{d x} (- \frac{1}{x ^{2}} + 1)

What is the solution for (x-1)dy+(y-x^2+2x^{-3})dx=0 ?
The solution for (x-1)dy+(y-x^2+2x^{-3})dx=0 is y=(x^3)/(3(x-1))+1/(x^2(x-1))+(c_{1})/(x-1)