What is the solution for (dx)/(dt)=(2-x)(1-t) ?

The solution for (dx)/(dt)=(2-x)(1-t) is x=-e^{-t+(t^2)/2-c_{1}}+2

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(dx)/(dt)=(2-x)(1-t)

\frac{d x}{d t} = (2 - x) (1 - t)

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

Solution steps

\frac{d x}{d t} = (2 - x) (1 - t)

Solve separable ODE:

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

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

\frac{y}{cos ( x )} \frac{d y}{d x} = \frac{1}{2}

\frac{d y}{d x} + 4 x y^{3} = 0, y (0) = \frac{1}{2}

\frac{d y}{d t} = - k y + 100 k, y (0) = 50

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

t x^{^{'}} = - t^{2} x^{3}

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