(a) Use Laplace transforms to solve the differential equation: 2d²y/dx²+5dy/dx-3y=0, given that when x =0, y=4 and dy/dx=9.

(b) In a galvanometer the deflection satisfies the differential equation: d²/dt²+2d/dt+=4. Use Laplace transforms to solve the equation forgiven that when t=0,=0and d/dt=0.

(c) The motion of a vibrating mass is given by d²y/dt²+8dy/dt+20y= 300sin4t. Show that the general solution of the differential equation is given by y=e^-4t (Acos2t+Bsin2t) + 15(sin4t-8cos4t)/13.