What is the solution for (dx)/(dt)=(a-b*t)x ?

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

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(dx)/(dt)=(a-b*t)x

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d}{d x} ((x^{2} + x)^{2})

n = 0 \sum \infty \frac{n ^{5}}{5 ^{n}}

t \to - 1 lim (ln (t + 2))

y = \frac{z ^{2} + 1}{z ^{2} - 1}

x \to - \infty lim (\frac{x - 8}{x ^{2} + 6})

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