變數可分離 O.D.E
1. xy'-y = y/lny-lnx , y(2)=2
Ans: y=x*exp[(2lnx-2ln2)^1/2]
2. dy/dx = (3xsin2y-2y)/(x-2x^2*cos2y)
ANS: x^2*y-x^3*sin2y=c
3. dy/dx =e^x*siny/y-2e^x*cosy ,y(0)=3π/2
ANS: -ycosy+siny-e^x*sin^2(y)= -2
Ans: y=x*exp[(2lnx-2ln2)^1/2]
2. dy/dx = (3xsin2y-2y)/(x-2x^2*cos2y)
ANS: x^2*y-x^3*sin2y=c
3. dy/dx =e^x*siny/y-2e^x*cosy ,y(0)=3π/2
ANS: -ycosy+siny-e^x*sin^2(y)= -2
請高手能詳析告知 這3題 一些解題目方向嗎??
好謝謝