Please check to see if the following seven questions i've answered are correct and explain your given answer. Thank you :)

The particular solution of the differential equation "Y = 12x2 satisying the boundary condition when x = 0, y = 1 and x = 3, y = 8 is Oy= x +2x+1 O y= x4 - 3x+1 Oy= x4 + 14 7x+1 Oy=x - #x+1 Oy= x - 4x+1The particular solution of the differential equations = 5x2 + 2 satisying the boundary condition when x = 3, y = 5 is Oy=. (3 + 2x - 5 Ov= 2x + 2x - 51 Oy= ex' + 2x - 46 Oy= Ex' + 2x - 3 Oy= x' + 2x - 45The particular solution of the differential equation " = 8 + csc t satisfying the boundary condition v ($ ) = -7 is Ov= 4x2 + cott + 7+12 Ov= 4x2 + cott - 7 - 12 Ov= 4x2 - cott - 7+ 12 Ov = 4x2 - cott - 7 - 12 Ov= 4x2 - cott + 7+ 12The particular solution of the differential equation dy dx 2 = 2 - 6x satisfying the boundary conditions when y (0) = 4 and >(0) = 1 is Ov=-x + x - 4x +1 Ov=-x + x2 - 4x - 1 Ov=x+x2 - 4x + 1 Ov=-x3 +x2 + 4x + 1 I + x + + z x + x = 10The particular solution of the differential equation #2 = 8t - 3 satisfying the initial conditions " | = = 4 and s(0) = 1 is O + 12 - 4t + 1 S = 312 + 41 + 1 C S = 3+2 - 41 + 1 S = 21- + 41 -1 Now N/ + + 12 + 4t+ 1The particular solution of the differential equation