What is the solution for (dy)/(dx)=2a-2by ?

The solution for (dy)/(dx)=2a-2by is y=-(e^{-2bx-c_{1}b})/b+a/b

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(dy)/(dx)=2a-2by

\frac{d y}{d x} = 2 a - 2 b y

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

Solution steps

\frac{d y}{d x} = 2 a - 2 b y (x)

Solve separable ODE:

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

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

y^{^{'}} - 3 y = 9, y (1) = 6

- y^{^{'}} - 3 y = 0

y^{^{'}} = \frac{2 x ^{3}}{y ^{4}}, y (0) = 3

y^{^{'}} = \frac{y}{x} - \frac{( y ^{2} )}{x}

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

What is the solution for (dy)/(dx)=2a-2by ?
The solution for (dy)/(dx)=2a-2by is y=-(e^{-2bx-c_{1}b})/b+a/b