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  • If dy/dx - y log 2 =2^sin x(cos x -1 ) log 2 , then

If dy/dx - y log 2 =2^sin x(cos x -1 ) log 2 , then

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best_answer

solution:   

            fracmathrmd ymathrmd x-ylog_e2=2^sin x(cos x-1 )log_e2

              This is Linear differential equation

            I.F=e^-log_e2int dx=e^-xlog_e2=2^-x

         Solution is

  Rightarrow        y2^-x=int 2^-x2^sin x(cos x-1 )log_e2hspace0.2cmdx

       Put    sin x-x=tRightarrow (cos x-1 )dx=dt

  Rightarrow         y2^-x=log_e2int 2^tdt=2^t+c

  herefore              y=2^x+t+c2^x=2^sin x+c2^x

Posted by

Deependra Verma

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