Thread: find the general solution

I am suppose to find a small integral root of the characteristic equation by inspection; then factor by division; and find the general solution of

y^(4) + y^(3) -3y''-5y'-2y=0

I am having problem with the first part of this trying to find the integral root, can someone please help me??

Thanks

Originally Posted by mandy123

I am suppose to find a small integral root of the characteristic equation by inspection; then factor by division; and find the general solution of

y^(4) + y^(3) -3y''-5y'-2y=0

I am having problem with the first part of this trying to find the integral root, can someone please help me??

Thanks

So our auxillary equation is



From the rational roots theorem we know the only possible rational roots are

so we only have 4 things to check

so m-2 is a factor

so by long or synthetic division we get



we notice that this is the binomial expansion of

so we end up with

so the solution is