(dy)/(dx)+50y= 1/2 ,y(0)=0

解答

\frac{d y}{d x} + 50 y = \frac{1}{2}, y (0) = 0

y = - \frac{e ^{- 50 x}}{100} + \frac{1}{100}

求解步骤

\frac{d y}{d x} + 50 y = \frac{1}{2}

求解可分离方程:

y = - \frac{e ^{- 50 x}}{100} + \frac{1}{100}

y = - \frac{e ^{- 50 x}}{100} + \frac{1}{100}

y^{^{'}} = 8 t - 10 t - 2 t \cdot y

\frac{d}{d x} (x y) = cot (x) y

y^{^{'}} - e^{y} x = 0

x \cdot \frac{d y}{d x} = \frac{1}{y ^{3}}

y^{^{'}} = x^{6} y^{- 5}