Question

求微分方程的通解 y''=e^y

Answer 1

e^y=y'' = d(y')/dx = d(y')/dy * dy/dx = y'd(y')/dy,

y'd(y') = e^ydy,

d[(y')^2] = d[2e^y],

2e^y + C^2 = (y')^2, C 为任意常数.

y' = [2e^y + C^2]^(1/2)或y'=-[2e^y+C^2]^(1/2),

(1...