What is the solution for xdy=(y^2-3y+2)dx ?

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

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xdy=(y^2-3y+2)dx

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (7)

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

\frac{d y}{d x} = e^{x - 2 y} + \frac{1}{e ^{2 y}}

\frac{d y}{y} + (\frac{1}{x} + 1) d x = 0

3 x y^{^{'}} - 5 y = 0, y (1) = 2

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