Find the general solution of differential equation 1, y '= 2xe (- y) 2, y' = x + y 3, 3Y '' + 2Y '- y = 0.4, y' '- 2Y' + 2Y = 2e (- x) The ones in brackets are all at the top right of the letter. Because I don't know how to type it-

Find the general solution of differential equation 1, y '= 2xe (- y) 2, y' = x + y 3, 3Y '' + 2Y '- y = 0.4, y' '- 2Y' + 2Y = 2e (- x) The ones in brackets are all at the top right of the letter. Because I don't know how to type it-

one
e^ydy=2xdx
So e ^ y = x ^ 2 + C
two
y'-y=x
The characteristic equation R-1 = 0
r=1
A special solution is y * = - X
So the general solution is y = CE ^ X-X
three
Characteristic equation 3R ^ 2 + 2r-1 = 0
We get R1 = 1 / 3, R2 = - 1
So the general solution y = C1E ^ (x / 3) + c2e ^ (- x)
four
Characteristic equation R ^ 2-2r + 2 = 0
R 1,2 = 1 ± I
A special solution y * = 2E ^ (- x) / 5
So the general solution is y = e ^ x (c1cosx + c2sinx) + 2E ^ (- x) / 5