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Homework Statement
Find the general solution to the differential equation:
y' - y = sinx + cos(2x)
Homework Equations
The Attempt at a Solution
r - 1 = 0
r = 1
y1 = c1e^x
i don't really understand how to pick the yp... do you just guess? i tried both Asinx + Bcos(2x) and Acosx -2Bsin(2x), and neither really worked out... but i may be doing it all wrong. my teacher went over it quickly, and our book doesn't cover it.
Homework Statement
show by means of the wronskian, that the second order differential equation y" + a1(x)y' + a0(x)y = 0 cannot have three linearly independent solutions y1, y2, y3.
The Attempt at a Solution
i have no attempt on this problem, because i have no idea what to do. i know how to do the wronskian (just the determinant), but that proves absolutely nothing.
thank you for any help!