Question

微分方程好难啊

Answer 1

你好，如图这是这道题的过程。你先求出齐次方程的解，然后再根据解的情况设出特解，最后用待定系数法把系数解出来就可以了。然后根据题目条件可以算出C1和C2

追答

Answer 2

f''(x) +f(x) = x^2

The aux. equation
p^2 +1=0
p=i or -1
yg= Acosx +Bsinx
let
yp = Cx^2+Dx+E
yp''=2C
yp'' +yp = x^2

2C +Cx^2+Dx+E =x^2
Cx^2 +Dx +(2C+E)=x^2
=>
C=1 and D=0 and 2C+E=0
C=1 and D=0 and E=-2
yp=x^2-2
通解
f(x) =yg+yp=Acosx +Bsinx +x^2-2
f(0)=0

A-2 =0
A=2
f(x) =2cosx +Bsinx +x^2-2
f'(x) =-2sinx +Bcosx +2x
f'(0) =1
B=1
ie
f(x) =2cosx +sinx +x^2-2