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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

`(23)/(18)`

B

`(13)/(6)`

C

`(25)/(9)`

D

`(31)/(18)`

Text Solution

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The correct Answer is:
D
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DISHA PUBLICATION-DIFFERENTIAL EQUATIONS -Exercise-2 : Concept Applicator
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  12. The solution of differential equation (dy)/(dx) = e^(x-y) + x^(2)e^(-y...

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  14. Solution of the differential equation (1+e^(x/y))dx + e^(x/y)(1-x/y)dy...

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  16. The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2), is

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  17. The solution of the differential equation x^(3)(dy)/(dx)+4x^(2) tany=e...

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  18. Solution of the differential equation ((x+y-1)/(x+y-2))(dy)/(dx)=((x+y...

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  19. Solve (1+e^((x)/(y)))dx + e^((x)/(y)) (1-(x)/(y))dy = 0

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