this is my question. thank you.

The general solution to the second order linear homogenous DE y" + y' -2y =O is 5 The general solution to the differential equation dy _ xy2 = 0 is dx O AeLX + Be -X, A, BER Ae2X + Bex, A, BER , CER C+ - O V= Ae -2X + Be*, A,BER O V= - 2 2. CER Acos(2x) + Bsin(2x), A, BER O y= Ae* + Be-2X, A,BE R none of these answers is correct 2. O -x2 (Hint for this question: a DE is linear/separable if it can be rearranged into the correct form.) e 2 , AER The first order DE V' = xy - x + 2y -2 is not linear and not separable none of these answers is correct linear and separable linear and not separable separable and not linear 6. The general solution to the second order homogeneous DE y" - 6y' + 9y = 0 is 3 An integrating factor for the first order linear DE y'+ 2xy = cos(In x) is O y= Ae SX + Bxe3X, A, BER 1( x ) = e-x2 O V = Acos(3x) + Bsin(3x), A,BER 1( x ) = ex 2 none of these answers is correct I(x) = e cos(In x) O V = Acos(3x) - Bsin(3x), A, BER O I(x ) = e2x O y= Aex + Be-3X, A,BER 1( x) = 1 4. The general solution to the DE Y' + V = sinx Ov= C+sinx CER X OV= C-Xcosx, CER none of these answers is correct OV= - C- COSX CER X Oy= _ C+ Cost CER X