(dy)/(dx)+9xy=8x,y(0)=5

解答

\frac{d y}{d x} + 9 x y = 8 x, y (0) = 5

y = \frac{37 e ^{- \frac{9 x ^{2}}{2}}}{9} + \frac{8}{9}

求解步骤

\frac{d y}{d x} + 9 x y = 8 x

求解可分离方程:

y = \frac{37 e ^{- \frac{9 x ^{2}}{2}}}{9} + \frac{8}{9}

y = \frac{37 e ^{- \frac{9 x ^{2}}{2}}}{9} + \frac{8}{9}

x^{^{'}} = a x (1 - \frac{x}{k})

y^{^{'}} sin^{2} (x) = cos (x) (1 - 3 y)

y^{^{'}} = \frac{y + 5}{7 t + 50}, y (2) = 0

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

\frac{1500}{230} (1 - 30 x^{^{'}}) = \frac{x}{0.1} + 75 x^{^{'}}