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## Homework Statement

Find the general solution of [itex]y^{(5)}-y(1)=x[/itex]

## The Attempt at a Solution

I found the complementary function by substitution of the solution form [itex]y=e^{kx}[/itex] giving [itex]k=0,1,-1,i,-i[/itex], so [itex]y_{cf}=a_0+a_1e^x+a_2e^{-x}+a_3e^{ix}+a_4e^{-ix}[/itex]

Now for the particular integral, the general trial solution form of a forcing term of x on the right is [itex]y=b_0+b_1x[/itex]

However if I plug this in, I get [itex]-b_1=x[/itex] !

I admit that I am not too familiar with dealing with differential equations of order greater than two. It seems that the general form of particular integrals when you have higher order ODEs has to be different? Or is the problem the fact that I already have a constant term in my complementary function sot here will not be a constant term in the particular integral too?

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