y^'=(1-13x)y^2,y(0)=-1/4

解答

y^{^{'}} = (1 - 13 x) y^{2}, y (0) = - \frac{1}{4}

y = - \frac{2}{2 x - 13 x ^{2} + 8}

求解步骤

y^{'} (x) = (1 - 13 x) y^{2}

求解可分离方程:

y = - \frac{2}{2 x - 13 x ^{2} + 8}

y = - \frac{2}{2 x - 13 x ^{2} + 8}

y^{^{'}} + \frac{y}{6} = 5, y (- 1) = 0

100 y + 0.01 y^{^{'}} = 500

\frac{d y}{d x} y = 7 x^{3}

\frac{d Q}{d t} + \frac{1}{50} Q = 0.2

y = (t^{2} - 20 t + 84) y^{^{'}}