(dy)/(dx)=(7-3x)e^{-y}

解答

\frac{d y}{d x} = (7 - 3 x) e^{- y}

y = ln (7 x - \frac{3 x ^{2}}{2} + c_{1})

求解步骤

\frac{d y}{d x} = (7 - 3 x) e^{- y}

求解可分离方程:

y = ln (7 x - \frac{3 x ^{2}}{2} + c_{1})

y = ln (7 x - \frac{3 x ^{2}}{2} + c_{1})

y^{^{'}} + 0.5 y = 3

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

x^{^{'}} = 2 + x + \frac{1}{4} x - \frac{1}{2}

e^{y} \cdot y^{^{'}} = \frac{3 x ^{2}}{1 + y}

\frac{d x}{d t} = - \frac{x}{100} + 125