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Let f(x) be differentiable on the interv...

Let `f(x)` be differentiable on the interval `(0,oo)` such that `f(1)=1` and `lim_(t->x) (t^2f(x)-x^2f(t))/(t-x)=1` for each `x>0`. Then `f(x)=`

A

`(1)/(3x) +(2x^(2))/(3)`

B

`-(1)/(3x) +(4x^(2))/(3)`

C

`-(1)/(x) +(2)/(x^(2))`

D

`(1)/(x)`

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The correct Answer is:
A
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ML KHANNA-DIFFERENTIAL EQUATIONS-Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
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  3. Solution of the differential equation (1+x^(2)) (dy)/(dx)+y=tan^(-1)x...

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  4. Solution of the differential equation 2y sin x (dy//dx)=2 sin x cos ...

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  5. The Solution of the equation (dy)/(dx)+2y=sin x is

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  6. The Solution of the equation (dy)/(dx)+y tan x =sec x is

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  7. The Solution of the equation x log x (dy)/(dx) +y = 2 log x is

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  8. Solution of the differential equation x(dy)/(dx)+2y=x^(2)logx is

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  9. The Solution of the equation (1+x^(2)) (dy)/(dx)+2xy -4x^(2)=0

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  10. The solution of differential equation (dy)/(dx)-3y= sin 2x is

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  11. The solution of the equation (dy)/(dx)+3y=cos^(2)x is

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  12. The gradient of the curve passing through (4,0) is given by (dy)/(dx) ...

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  13. Solution of the differential equation sin2x (dy)/(dx) -y=tan x is

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  14. The Solution of the differential equation (dy)/(dx) +(1)/(x)tan y =(1...

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  15. Solution of the equation (dy)/(dx) = e^(x-y) (e^(x)-e^(y)) is equal t...

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  16. If y(t) is solution of (t+1)(dy)/(dt) -ty =1, y(0)= -1. At t = 1 the s...

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  17. The solution of differential equation (dy)/(dx)(x^(2)y^(3)+xy) =1 is...

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  18. The solution of the differential equation (dy)/(dx)-(x log x)/(1+log...

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  19. If (dy)/(dx)+Py=Q where P and Q are functions of x alone then integrat...

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  20. Let f(x) be differentiable on the interval (0,oo) such that f(1)=1 and...

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