Please solve.

. Consider the differential equation ry'ty =x. Without solving the equation, check which of the following are solutions: y(x) = sin(x). y() = y(x) = VI. y(x) = That is: do not use the method of integrating factors to solve. Just check by plugging in. . Consider the differential equation y' = x(1+y' ). Which of the following are solutions. y(x) = x- +3. y(x) = tan 3 + 2 y(x) = Vx3+1. . Solve the initial value problems ry'+ (x + 1 )y =0, y(1) = 2, and (1 + r )y - 2xy = 0, y(0) = 3. . Solve the initial value problems y + 3y = 1, y(0) = 1, y' + 2ry = re-> y(0) = 2. 1 + 7y =ek y(0) = 0, ry + 2y = 8x2 y (1) = 3.\f