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PRADEEP KUMAR Grade:
        a.) solve:dy/dx+(2x+(tan^-1y)-(x^3))(1+y²)=0


b.) A particle of unit mass moves in a straight line in a resisting medium which produces resistance kV.If the particle starts with a velocity u from the position S=Sa,show that , as time goes on , the particle approaches the position S=Sa+(u/k).
6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

ans a)  dy/dx  + [2x + (tan-1y)- (x3) ][1+y2]


 


 now divide the equation by 1+y2


        dy/dx(1/1+y2)  +  [2x + tan-1y - x3 ]       ................1


 


now put tan-1y=t


 differentiate wrt x


          dy/dx(1/1+y2) =dt/dt .............2


now substitute 2 in 1


so


       dt/dx + t +2x-x3 = 0


this eq is linear differential equation and its integral factor is ex ...


now u can solve this easily...

6 years ago
vikas askiitian expert
510 Points
										

retardation of particle = kv


                  a=kv ..............1


       a=dv/dt   &   v=dx/dt


 putting these eq 1 becomes


                dv/dt = kds/dt


                dv =k ds


 now integrate both sides by taking proper limits


            u-0= k(s-sa)


             s-sa =u/k       or


             s= sa+u/k

6 years ago
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