unsolvable differential equation ?

• Jul 28th 2008, 04:25 AM
DE novice
unsolvable differential equation ?
This one doesn't seem too hard but I've tried every which way to solve....even put it in MatLab and its spits out an error message "too many levels of recursion"...I can't get it. Anyone see the trick ? (Crying)

y"-2y'-y=exp^(2t)-exp^(t)
• Jul 28th 2008, 04:45 AM
mr fantastic
Quote:

Originally Posted by DE novice
This one doesn't seem too hard but I've tried every which way to solve....even put it in MatLab and its spits out an error message "too many levels of recursion"...I can't get it. Anyone see the trick ? (Crying)

y"-2y'-y=exp^(2t)-exp^(t)

Solve y'' - 2y' - y = 0 to get the homogenous solution. This is a second order DE with constant coefficients. y = A e^(1 + sqrt{2})t + B e^(1 - sqrt{2})t.

Get particular solutions for e^(2t) and - e^t. Assume particular solutions of the form a e^(2t) and b e^t. Substitute into DE and solve for a and b.

Add the particular solutions to the homogenous solution to get the general solution.