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

(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.

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