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).

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vikas askiitian expert · Answer

ans a) dy/dx + [2x + (tan -1 y)- (x 3 ) ][1+y 2 ] now divide the equation by 1+y 2 dy/dx(1/1+y 2 ) + [2x + tan -1 y - x 3 ] ................1 now put tan -1 y=t differentiate wrt x dy/dx(1/1+y 2 ) =dt/dt .............2 now substitute 2 in 1 so dt/dx + t +2x-x 3 = 0 this eq is linear differential equation and its integral factor is e x ... now u can solve this easily...

vikas askiitian expert · Answer

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-s_a)

s-s_a =u/k or

s= s_a+u/k

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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).

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).

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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).

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).

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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).