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The integrating factor of the differenti...

The integrating factor of the differential equation `(dy)/(dx)+(y)/((1-x)sqrt(x))=1-sqrt(x)`, is

A

` (1+sqrt(x))/(1-sqrt(x))`

B

` (1-sqrt(x))/(1+sqrt(x))`

C

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

D

`(sqrt(x))/(1-sqrt(x))`

Text Solution

Verified by Experts

The correct Answer is:
b
Given `(dy)/(dx) + y/(1-xsqrt(x)) = 1 - sqrt(x)`
` :. IF e^(int 1/(1-x)sqrt(x)dx)`
Put `sqrt(x) = t`
` rArr 1/(2sqrt(x))dx = dt`
` :. If = e^(int2/(1-t^(2)dt)) = e ^(2/2 log.((1+1)/(1-t)) )`
` = ((1+1)/1-t)= (1+sqrt(x))/(1-sqrt(x))`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. The solution of the differential equation (1+y^2)+(x-e^(tan^-1y))dy/dx...

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  2. The solution of the differential equation (dy)/(dx)=(x+y)/x satisfyi...

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  3. The integrating factor of the differential equation (dy)/(dx)+(y)/((1-...

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  4. The solution of the differential equation (dy)/(dx)-y tan x=e^(x)sec x...

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  5. (1 + x^(2)) (dy)/(dx) + 2xy = 4x ^(2), given that y = 0, when x =0

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  6. The solution of the differential equation x(dy)/(dx) = 2y + x^(3)e^(x...

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  7. The solution of the differential equation (dy)/(dx) = y tan x - 2 si...

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  8. The family of curves y = e^(a sinx) where a is an arbitrary constant ...

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  9. The differential equation of the family y = ae^(x) + bx e^(x) + cx^(2)...

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  10. The order and degree of the differential equation of all tangent lin...

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  11. The general solution of y^(2)dx+(x^(2)-xy+y^(2))dy=0, is

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  12. The general solution of the differential equation (dx)/(dy)+(x/y)^2-...

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  13. The general solution of the differential equaiton (1+y^(2))dx+(1+x^(2)...

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  14. The solution of (dy)/(dx)+1 = e^(x+y) is

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  15. The differential equation (dy)/(dx) = (x(1+y^(2)))/(y(1+x^(2)) repres...

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  16. If xsin((y)/(x))dy=[ysin((y)/(x))-x]dx ad y(1)=(pi)/(2), then the valu...

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  17. Solution of the differential equation tan y.sec^(2) x dx + tan x. sec^...

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  18. The solution of e^(dy//dx) = (x+1) , y (0) = 3 is

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  19. Solution of the differential equation x((dy)/(dx))^(2)+2sqrt(xy)(dy)...

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  20. If C is an arbitrary constant , then the general solution of the diffe...

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