What is the solution for y^'=-2x(y^2-3y+2) ?

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

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y^'=-2x(y^2-3y+2)

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

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

Solution steps

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

Solve separable ODE:

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

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

(x^{2} + 4) y^{^{'}} = 2 x y

cos^{2} (x) \frac{d y}{d x} = y^{2} sin^{2} (x)

(- y - 2) d x + (x - 2) d y = 0

\frac{d x}{d t} x = t^{2} - 5

\frac{d y}{d t} = 100 - y, y (0) = 20

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