What is the solution for (dx)/(dt)=-(11x)/((1000-t)) ?

The solution for (dx)/(dt)=-(11x)/((1000-t)) is

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(dx)/(dt)=-(11x)/((1000-t))

\frac{d x}{d t} = - \frac{11 x}{( 1000 - t )}

x = 100 0^{11} e^{c_{1}} - 100 0^{10} \cdot 11 e^{c_{1}} t + 100 0^{9} \cdot 55 e^{c_{1}} t^{2} - 100 0^{8} \cdot 165 e^{c_{1}} t^{3} + 100 0^{7} \cdot 330 e^{c_{1}} t^{4} - 100 0^{6} \cdot 462 e^{c_{1}} t^{5} + 100 0^{5} \cdot 462 e^{c_{1}} t^{6} - 100 0^{4} \cdot 330 e^{c_{1}} t^{7} + 165000000000 e^{c_{1}} t^{8} - 55000000 e^{c_{1}} t^{9} + 11000 e^{c_{1}} t^{10} - e^{c_{1}} t^{11}

Solution steps

\frac{d x}{d t} = - \frac{11 x}{( 1000 - t )}

Solve separable ODE:

x = 100 0^{11} e^{c_{1}} - 100 0^{10} \cdot 11 e^{c_{1}} t + 100 0^{9} \cdot 55 e^{c_{1}} t^{2} - 100 0^{8} \cdot 165 e^{c_{1}} t^{3} + 100 0^{7} \cdot 330 e^{c_{1}} t^{4} - 100 0^{6} \cdot 462 e^{c_{1}} t^{5} + 100 0^{5} \cdot 462 e^{c_{1}} t^{6} - 100 0^{4} \cdot 330 e^{c_{1}} t^{7} + 165000000000 e^{c_{1}} t^{8} - 55000000 e^{c_{1}} t^{9} + 11000 e^{c_{1}} t^{10} - e^{c_{1}} t^{11}

x = 100 0^{11} e^{c_{1}} - 100 0^{10} \cdot 11 e^{c_{1}} t + 100 0^{9} \cdot 55 e^{c_{1}} t^{2} - 100 0^{8} \cdot 165 e^{c_{1}} t^{3} + 100 0^{7} \cdot 330 e^{c_{1}} t^{4} - 100 0^{6} \cdot 462 e^{c_{1}} t^{5} + 100 0^{5} \cdot 462 e^{c_{1}} t^{6} - 100 0^{4} \cdot 330 e^{c_{1}} t^{7} + 165000000000 e^{c_{1}} t^{8} - 55000000 e^{c_{1}} t^{9} + 11000 e^{c_{1}} t^{10} - e^{c_{1}} t^{11}

\frac{d y}{d x} = \frac{3}{( x ^{2} y - 8 y )}

(x^{2} - 9) \cdot y^{^{'}} + x \cdot y = 0

y^{^{'}} = 2 \cdot y + 1 \cdot cos (x)

2 x (y + 1) + (x^{2} + 6) \frac{d y}{d x} = 0

y^{^{'}} = - y, y (0) = 5

What is the solution for (dx)/(dt)=-(11x)/((1000-t)) ?
The solution for (dx)/(dt)=-(11x)/((1000-t)) is