Find the general solution of the given differential equation: y'''-y''-y'+y=0 Please help. Note: These are higher order Linear equations, homogeneous equation with constant coefficients.
\[y(x)=c_1 e^{-x}+c_2 e^x+c_3 e^x x \]
I think you can do like r^3 - r^2 - r + 1 = 0. Then find the roots of this equation. If it has distinct roots then what robtobey said I guess.
Do you know the exact step by step process that I will need to go through to get the answer? Thanks!
As i said: Set up like the equation I showed. Find the roots of that equation. It should have 3 roots. Case 1: 3 distinct roots > the result is like robtobey said. Case 2: repeat roots Case 3: complex roots, repeat complex roots etc... look at the case in your book. It should have examples.
Thanks for you help.
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