Problem solving

4. Show that y = Cue" + Caxe" + Cae * + 2x"e" is a primitive associated with the differential equation; d'y dx d'y y+y= Be. dx dx + 5. Determine whether (y - C) = Cx is a solution of the differential equations 4x(dy/dx) + 2x (dy/dx) - y = 0. 6. Determine C, and C2 so that y(x) = C sin 2x + C2 cos 2x + 1 will satisfy the conditions y(7 /8) = 0 and y(7 /8) = 2. 7 7. A general solution to a certain differential equations is y(x) = c1 e" + c3 xe + xe" In |x], where c1 and c3 are arbitrary constants. Find a particular solution which also satisfies the initial conditions y(1) = 0, y'(1) = 1. 8. Solve x' (y+1) dx + y'(x - 1)dy = 0