Inverse differential operators

[hbomb]

I need someone to check some homework problems that I've done so far regarding inverse differential operators.

1) 9y"-4y=sinx
yp=-1/13 sinx

2) y"-4y'-12y=x-6
yp=-1/12(x-6)

3) y'''+10y""+25y'=e^x
yp=36

4) y""+8y'=4
yp=1/2 x

5) y"-9y=54
yp=-6

6) y"-y'-12y=e^(4x)
yp=1/7 xe^(4x)

7) y"+25y=6sinx
yp=1/4 sinx

sorry for not converting the equations into the latex form but I'm kinda of in a hurry. thanks

 

[Fermat]

Substitute yp into each of your DE's and check that the lhs = the rhs.

 

[HallsofIvy]

3) y'''+10y""+25y'=e^x
yp=36

Surely you can see that this can't be right!