Question

求微分方程dy/dx+3y=8,在满足x=0,y=2 时的特解.

Answer 1

dy/dx+3y=8,

分离变量得

dy/(3y-8)=-dx,

ln|y-8/3|/3=-x+c,

把x=0,y=2代入得c=(1/3)ln(2/3),

∴ln(8/3-y)=-3x+ln(2/3),

ln(4-3y/2)=-3x,

4-3y/2=e^(-3x),

4-e^(-3x)=3y/2,

∴y=8/3-(2/3)e^(-3x).