I tried to solve 5 a) in two different methods I don't know which one is correct.

I also want to know whether I wrote 5 b answer correctly

5. * Solve the following differential equations: (a) da-2 - y = rez (b) (xcosy + x2 +y) de+ (xty? - , sing) dy = 0 a) dy docz - y = x1 es y" - y = des y ( c ) = ynbc) + yp ( 20 ) yn () : homogeneous solution to the linear DE ypcc ) : particular solution for the term "cel 72 1=0 = (2+1 (1-1)=0 Up = U, ( x ( ) y, + Uzac) yz = Ulic)e" + Us (>()ex y " p = U,' luc) e " - Us (cle"tu, (() e" + u, we"* = ville"-u,'boe"=xe 2 - = ) 0,60 ) = me Up = - (2+2 )e's + (3x(+2) e-52/2 = -(2(+) e1 9 2 -571/2 [- wet = (3x+2 )-3/2 95. * Solve the following differential equations: (a) dry_ 2- y = xel (b) (xcosy +x2 + y) da + (x ty? - , siny) dy = 0 a ) dy doz - y = x es doc ? xezty dy =( xe tydil = 26 ( 2 ) e = +yx+ gly ) f ( 1(,y ) = [ 26 - 2 ) @ + you + gc y ) do = 4 6 ( - 4 ) e = + { yx + gly) x th ly) b ) M = ccosy tasty My = =using + IV N = D ty ? 2CE sing Nx= 1 - >csing v As My = Nic the differential equation is exact flocy ) = Saccosytac ty doc = > cosy+ 3 x try tgly ) fling ) = [ 20 ty - 2[ singdy = xy + y' -2-cosyth() gly ) = zyb "(( ) = 3x + 2"cosy " cosy + 570' t xy +by = Page 7 of 10 11