(y/x) • dy/dx + e^y = 0
dy/dx = - xe^y/y
∫ ye^(-y) dy = - ∫ x dx
- ∫ y de^(-y) = - ∫ x dx
- ye^(-y) + ∫ e^(-y) dy = - ∫ x dx
- ye^(-y) - e^(-y) = - x²/2 + C
- (1 + y)e^(-y) = - x²/2 + C
用隐函数表示吧,很难解出y
求微分方程通解 (y/x)y'+e^y=0
(y/x) • dy/dx + e^y = 0
dy/dx = - xe^y/y
∫ ye^(-y) dy = - ∫ x dx
- ∫ y de^(-y) = - ∫ x dx
- ye^(-y) + ∫ e^(-y) dy = - ∫ x dx
- ye^(-y) - e^(-y) = - x²/2 + C
- (1 + y)e^(-y) = - x²/2 + C
用隐函数表示吧,很难解出y