What is the solution for (dy)/(dx)=y-x,y(0)= 2/3 ?

The solution for (dy)/(dx)=y-x,y(0)= 2/3 is y=x+1-1/3 e^x

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(dy)/(dx)=y-x,y(0)= 2/3

\frac{d y}{d x} = y - x, y (0) = \frac{2}{3}

y = x + 1 - \frac{1}{3} e^{x}

Solution steps

\frac{d y}{d x} = y - x

Solve linear ODE:

y = x + 1 - \frac{1}{3} e^{x}

y = x + 1 - \frac{1}{3} e^{x}

\int \frac{2 x + 1}{( x - 1 ) ( x + 3 )} d x

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

\frac{\partial}{\partial y} (e^{- 2 y} cos (x))

\frac{d}{d x} ((x - 1) (x^{2} - 8 x + 7))

y = 5 cos (2 x), y = 5 sin (4 x), x = 0, x = \frac{π}{4}

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