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A function satisfying int0^1f(tx)dt=nf(x...

A function satisfying `int_0^1f(tx)dt=nf(x)`, where `x>0` is

A

`f(x) =c.x^(1-n/n)`

B

`f(x) =c.x^(n/n-1)`

C

`f(x) =c.x^(1/n)`

D

`f(x) =c.x^(1-n)`

Text Solution

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The correct Answer is:
A
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MOTION-DIFFERENTIAL EQUATION -Exercise 2
  1. The equation of the curve passing through origin and satisfying the di...

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  2. passes through a curve point (1,pi/4) and at some point Its gradation ...

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  3. A function satisfying int0^1f(tx)dt=nf(x), where x>0 is

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  4. The general solution of the differential equation (dy)/(dx)+(1+cos2y)/...

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  5. The solution of the differential equation (dy)/(dx)=(xy)/(x^2+y^2) is

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  6. The solution of differential equation (1+y^(2))+(x-e^(tan^(-1)y))(dy...

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  7. The solution of the differential equation, e^x(x +1)dx + (ye^y -xe^x)d...

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  8. The solution of y^5x+y-x dy/dx=0 is

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  9. The solution of the differential equation x^2(dy)/(dx)cos1/x-ysin1/x=-...

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  10. The solution of (dy)/(dx) + y tan x = sec x is

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  11. Solution of the differential equation (dy)/(dx)+ytanx=x^(n)cosx is

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  12. (dy)/(dx)+(3x^2)/(1+x^3)y=(sin^2x)/(1+x^3)

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  13. Solution of the equation (1 - x^2) dy + xy dx = xy^2dx is

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  14. Solve the differential equation (y^2+x^2)dx=(x^2+xy)dy

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  15. Find the particular solution of (cos x – x sin x +y^2)dx + 2xy dy = 0 ...

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  16. Orthogonal trajectories of family of the curve x^(2/3)+y^2/3=a^((2/3))...

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  17. The curve in the first quadrant for which the normal at any point (...

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  18. A curve C passes through origin and has the property that at each poin...

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  19. Water is drained from a vertical cylindrical tank by opening a valv...

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  20. If y=x/(In|cx|) (where c is an arbitrary constant) is the general solu...

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