What is the solution for (dx)/(dt)=x-ax ?

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

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(dx)/(dt)=x-ax

\frac{d x}{d t} = x - a x

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

Solution steps

\frac{d x}{d t} = x - a x (t)

Solve separable ODE:

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

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

y = t^{2} ln (t^{2}) \frac{d y}{d t}

\frac{d x}{d t} = 4 x t

(\frac{y}{x})^{2} \frac{d y}{d x} = y^{3} - 1

\frac{d y}{d x} = \frac{3 x ^{2} - 4 x - 1}{2 y - 4}

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

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