Consider a nonhomogeneous linear equation of the formthat is, b(t) is written as a sum of...

Consider a nonhomogeneous linear equation of the form

that is, b(t) is written as a sum of two functions. Suppose that yh(t) is a solution of the associated homogeneous equation dy/dt + a(t)y = 0, that y1(t) is a solution of the equation dy/dt + a(t)y = b1(t), and that y2(t) is a solution of the equation dy/dt +a(t)y = b2(t). Show that yh(t)+ y1(t)+ y2(t) is a solution of the original nonhomogeneous equation.