方程：x一点（就是X头上一点）=tx,给出的答案是x(t)=x(t0--就是t下标0)e^(0.5*t^2),

Question

方程：x一点（就是X头上一点）=tx,给出的答案是x(t)=x(t0--就是t下标0)e^(0.5*t^2),

Answer 1

dx/dt = tx =>dx/x = tdt
两边积分=>lnx = 1/2*t^2 +c
=>x = lnc*e(1/2*t^2) 当t=0时,x(t0) = lnc
x(t0) =xt0 => x(t) = x(t0) e(1/2*t^2)