解微分方程af(x)＋bf'(x)＝ca,b,c是常数求f(x)

Question

解微分方程a f(x)＋bf'(x)＝c a,b,c是常数 求f(x)

Answer 1

a f(x)＋bf'(x)＝c
f'(x)＝c/b-a f(x)/b
f(x)=pe^(mx)+nx+k
f'(x)=[pe^(mx)+nx+k]'=mpe^(mx)+n=m[pe^(mx)+nx+k]-mnx+n-mk
m=-a/b;
mn=0,n=0;
n-mk=c/b,k=-c/(bm)=c/a
f(x)=-ape^(-ax/b)/b+c/a=Ce^(-ax/b)+c/a