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The solution of the differential equatio...

The solution of the differential equation `(dy)/(dx) = 1/(x+y^(2))` is

A

`y = -x^(2) - 2x - 2 +Ce^(x)`

B

`y = x^(2) + 2x +2 - Ce^(x)`

C

` x = -y^(2) - 2y + 2 - Ce^(y)`

D

` x = -y^(2) - 2y - 2 +Ce^(y)`

Text Solution

Verified by Experts

The correct Answer is:
d
Given differential equation is
` (dy)/(dx) = 1/(x+y^(2))`
` rArr (dx)/(dy)- x = y^(2)`
Here, `P = -1 , Q = y^(2)`
` :. IF = e^(int - dy) = e^(-y)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. The solution of differential equation [ e^(-2sqrt(2))/(sqrt(x))-y/(...

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  2. The integrating factor of the differential equation (y log y) dx = (l...

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

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  4. Integrating factor of the differential equation (x.logx)(dy)/(dx)+y=2l...

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  5. Solution of the equation x^(2)y - x^(3)(dy)/(dx)=y^(4)cosx , when y(0)...

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

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

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

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

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  10. (1 + x^(2)) (dy)/(dx) + 2xy = 4x ^(2), given that y = 0, when x =0

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

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

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

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

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

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

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

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

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

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

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