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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).
```
6 years ago

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
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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