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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!