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Popular >

(dx)/(dt)=1-x-x^2

Solution

\frac{d x}{d t} = 1 - x - x^{2}

Solution

x = \frac{e ^{5 t + 5 c_{1}}}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{5 e ^{5 t + 5 c_{1}}}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{5}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{1}{2 ( 1 - e ^{5 (t + c_{1})} )}

Solution steps

\frac{d x}{d t} = 1 - x - x^{2}

Solve separable ODE:

x = \frac{e ^{5 t + 5 c_{1}}}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{5 e ^{5 t + 5 c_{1}}}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{5}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{1}{2 ( 1 - e ^{5 (t + c_{1})} )}

x = \frac{e ^{5 t + 5 c_{1}}}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{5 e ^{5 t + 5 c_{1}}}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{5}{2 ( 1 - e ^{5 (t + c_{1})} )} - \frac{1}{2 ( 1 - e ^{5 (t + c_{1})} )}

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Frequently Asked Questions (FAQ)

What is the solution for (dx)/(dt)=1-x-x^2 ?
The solution for (dx)/(dt)=1-x-x^2 is