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If f'(x) = sqrt(x) and f(1) = 2 then f(...

If `f'(x) = sqrt(x)` and f(1) = 2 then f(x) is :

A

`2/3 (x sqrt(x)+2)`

B

`2/3 (xsqrt(x)+2)`

C

`3/2 (x sqrt(x)+2)`

D

`-2/3 (x sqrt(x)+2)`

Text Solution

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The correct Answer is:
B
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PREMIERS PUBLISHERS-ORDINARY DIFFERENTIAL EQUATIONS -PROBLEMS FOR PRACTICE (Choose the Correct Answer)
  1. The integrating factor of (dy)/(dx)+(1)/(xlogx)y= (2)/(x^(2)) is :

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  2. The degree of the differential equation (y' - 2y '' ) ^(2) = (y')^(4) ...

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  3. If f'(x) = sqrt(x) and f(1) = 2 then f(x) is :

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  4. The order and degree of the differential equation (d^(2)y)/(dx^(2))- y...

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  5. The differential equation of the family of lines y = mx is :

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  6. If (dy)/(dx)= (x-y)/(x+y) then its solution is :

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  7. The integrating factor for (dy)/(dx) - 2y tan x = cos x is :

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  8. The integrating factor of (dy)/(dx) +2 y/x = e^(4x) is :

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  9. Which of the following is a solution of (d^(2)y)/(dx^(2))+ y = 0 :

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  10. The differential equation formed by eliminating A and B for the relat...

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  11. If xy=a^(2) where a is arbitrary constant then :

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  12. The order and degree of the differential equation y'' (y - (y')^(3))...

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  13. The degree of the differential equation rho= (1+((dy)/(dx))^(2))^(3/2...

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  14. The order and degree of the differential equation ((dy)/(dx))^(2) = ...

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  15. The solution of the equation (dx)/(dy) + Px = Q where P and Q are func...

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  16. The degree of the differential equation (d^(2)y)/(dx^(2)) x = sqrt(y +...

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  17. If y^(2) = 4ax where a is constant then the differential equation for...

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  18. The differential equation formed if y = (A - Bx ) e^(-2x) is :

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  19. The differential equation that will represent the family of all circle...

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  20. Solve (x^(2)-y) dx+(y^(2)-x)dy=0 , if it passes through origin :

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