What is the solution for (dx)/(dt)=-0.1(x-100+40e^{-0.1t}) ?

The solution for (dx)/(dt)=-0.1(x-100+40e^{-0.1t}) is x=100-(4t)/(e^{0.1t)}+(c_{1})/(e^{0.1t)}

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(dx)/(dt)=-0.1(x-100+40e^{-0.1t})

\frac{d x}{d t} = - 0.1 (x - 100 + 40 e^{- 0.1 t})

x = 100 - \frac{4 t}{e ^{0.1 t}} + \frac{c _{1}}{e ^{0.1 t}}

Solution steps

\frac{d x}{d t} = - 0.1 (x - 100 + 40 e^{- 0.1 t})

Solve linear ODE:

x = 100 - \frac{4 t}{e ^{0.1 t}} + \frac{c _{1}}{e ^{0.1 t}}

x = 100 - \frac{4 t}{e ^{0.1 t}} + \frac{c _{1}}{e ^{0.1 t}}

x \to 2 - lim (ln ∣ x - 2 ∣)

\int \frac{1}{x ^{2} - y ^{2}} d y

f (x) = \frac{x ^{2} + 2 x - 6}{( x + 1 ) ^{2}}

x \to 0 - lim (e^{\frac{5}{x}})

x \to \infty lim (x^{- 4})

What is the solution for (dx)/(dt)=-0.1(x-100+40e^{-0.1t}) ?
The solution for (dx)/(dt)=-0.1(x-100+40e^{-0.1t}) is x=100-(4t)/(e^{0.1t)}+(c_{1})/(e^{0.1t)}