(y^3-1)exdx+3y^2(ex+1)dy=0

解答

(y^{3} - 1) e x d x + 3 y^{2} (e x + 1) d y = 0

y = 3 e^{- x - \frac{1}{e} + c_{1}} (e x + 1)^{\frac{1}{e}} + 1

求解步骤

(y^{3} - 1) e x d x + 3 y^{2} (e x + 1) d y = 0

求解可分离方程:

y = 3 e^{- x - \frac{1}{e} + c_{1}} (e x + 1)^{\frac{1}{e}} + 1

y = 3 e^{- x - \frac{1}{e} + c_{1}} (e x + 1)^{\frac{1}{e}} + 1

x \to 0 lim (4 x cot (x))

\int_{0}^{1} 8 e^{2 x} d x

d er i v a t i v e 2 e^{x} + \frac{8}{3 x}

\frac{d}{d x} (ln (x^{2} e^{- x}))

s l o p e x y - 2 y^{2} = 5, (11, 5)