Question

求解一阶微分方程(t-2y-4)dt+(2t-y-5)dy=0求y(t)=?

Answer 1

(t-2y-4)dt+(2t-y-5)dy=0dy/dt=(t-2y-4)/(2t-y-5)令Y=y+1 T=t-2代入：dY/dT=(T-2Y)/(2T-Y)=(1-2Y/T)/(2-Y/T)令u=Y/T Y=Tu dY/dT=u+Tdu/dTu+Tdu/dT=(1-2u)/(2-u)Tdu/dT=(1-2u)/(2-u)-u=(1-4u+u^2)/(2-u)(2-u)du/(...