What is the solution for (dx)/(dt)=-(10x)/(750-5t) ?

The solution for (dx)/(dt)=-(10x)/(750-5t) is x=22500e^{c_{1}}-300e^{c_{1}}t+e^{c_{1}}t^2

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(dx)/(dt)=-(10x)/(750-5t)

\frac{d x}{d t} = - \frac{10 x}{750 - 5 t}

x = 22500 e^{c_{1}} - 300 e^{c_{1}} t + e^{c_{1}} t^{2}

Solution steps

\frac{d x}{d t} = - \frac{10 x}{750 - 5 t}

Solve separable ODE:

x = 22500 e^{c_{1}} - 300 e^{c_{1}} t + e^{c_{1}} t^{2}

x = 22500 e^{c_{1}} - 300 e^{c_{1}} t + e^{c_{1}} t^{2}

\int sin^{4} (\frac{x}{3}) cos (\frac{x}{3}) d x

y^{5} = x^{6}

\frac{d}{d x} (\frac{- 0.4}{5 + 5 x})

\frac{d y}{d x} + 0.1 y = 10

\int_{1}^{2} \frac{3 ^{l n (x)}}{x} d x

What is the solution for (dx)/(dt)=-(10x)/(750-5t) ?
The solution for (dx)/(dt)=-(10x)/(750-5t) is x=22500e^{c_{1}}-300e^{c_{1}}t+e^{c_{1}}t^2