x^'=1-3x+2x^2

解

x^{^{'}} = 1 - 3 x + 2 x^{2}

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

解答ステップ

x^{'} (t) = 1 - 3 x + 2 x^{2}

分離可能 ODE を解く:

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

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