f✀(x)=f(x)+x^2 求解f(x)

2025-02-26 03:43:25
推荐回答(2个)
回答1:

f'(x)=f(x)+x^2
The aux. equation
p-1=0
p=1
let
yp = Ax^2+Bx+C
yp'=2Ax+B
yp' -yp = x^2
Ax^2+(B-2A)x+(-B+C) = x^2
coef. of x^2 => A=1
coef. of x
B-2A =0
B=2
coef. of constant
-B+C=0
C=2
yp = x^2+2x+2
ie
f(x) = De^x + x^2+2x+2

回答2:

f(x)=[e^(x)x^(3)]/3