x^'x=-1/2 (x^2-25)

解答

x^{^{'}} x = - \frac{1}{2} (x^{2} - 25)

x = e^{- t - c_{1}} + 25, x = - e^{- t - c_{1}} + 25

求解步骤

x^{'} (t) x = - \frac{1}{2} (x^{2} - 25)

求解可分离方程:

x = e^{- t - c_{1}} + 25, x = - e^{- t - c_{1}} + 25

x = e^{- t - c_{1}} + 25, x = - e^{- t - c_{1}} + 25

x \frac{d y}{d x} = \frac{1 - 5 y ^{2}}{3 y}

x^{2} e^{y} \frac{d y}{d x} + 2 x e^{y} = x

\frac{y d y}{d x} + 4 x^{2} + 6 x + 1 = 0

y^{^{'}} = e^{3 x - 4 y}, y (0) = 0

\frac{d y}{d x} + 9 x^{8} y = 0, y = 6 e^{- x^{9}}