用matlab解微分方程

楼主是要解析解吧

dsolve('Dy=A/V-B/V*sqrt(2*g*y)','y(0)=h0','t')

ans =

(2^(1/2)*A + 2^(1/2)*A*lambertw(0, (2^(1/2)*B*g^(1/2)*exp(-(A + B^2*g*(t/V - (A*(log(-(exp(-(A + 2^(1/2)*B*(g*h0)^(1/2))/A)*(2*B*(g*h0)^(1/2) + 2^(1/2)*A))/(2*B*g^(1/2))) + 1))/(B^2*g)))/A))/A))^2/(4*B^2*g)
(2^(1/2)*A + 2^(1/2)*A*lambertw(0, (2^(1/2)*B*g^(1/2)*exp(-(A + B^2*g*(t/V - (A*(log((exp(-(A - 2^(1/2)*B*(g*h0)^(1/2))/A)*(2*B*(g*h0)^(1/2) - 2^(1/2)*A))/(2*B*g^(1/2))) + 1))/(B^2*g)))/A))/A))^2/(4*B^2*g)

lambert w叫Ω函数或乘数对数,属于复变函数的范畴

所以还是用数值解的好