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  • If the solution of the equation d2x/dt2 +4 dx/dt +3x =0 given that for t=0 ,x=0 and dx/dt=12 is in the form x=Ae^-3t + B e^-t , then

If the solution of the equation d2x/dt2 +4 dx/dt +3x =0 given that for t=0 ,x=0 and dx/dt=12 is in the form x=Ae^-3t + B e^-t , then

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Solution:       x=Ae^-3t+Be^-t

                herefore       fracmathrmd xmathrmd t=-3Ae^-3t-Be^-t   

                   When    t=0 ,x=0

            Rightarrow         A+B=0           .........(1)

            At               t=0,fracmathrmd xmathrmd t=12

          herefore                12=-3A-B        .........(2)

           Sloving , we get       A=-6,B=6.

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Deependra Verma

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