y的二阶导数等于e的2y次方,求通解

2025-06-27 06:53:12
推荐回答(1个)
回答1:

y'' = e^2y
设 p=y',则 y'' = dp/dx = (dp/dy)*(dy/dx) = pdp/dy,
代入得 pdp = e^2y dy,
乘以 2 并积分得 p^2 = e^2y + C1,
所以 dy/dx = √(e^2y+C1),