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A family of curves has the differential ...

A family of curves has the differential equation `xy(dy)/(dx)=2y^(2)-x^(2)`. Then, the family of curves is

A

`y^(2)=cx^(2)+x^(3)`

B

`y^(2)=cx^(4)+x^(2)`

C

`y^(2)=x+cx^(4)`

D

`y^(2)=x^(2)+cx^(4)`

Text Solution

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The correct Answer is:
B
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SIA PUBLICATION-DIFFERENTIAL EQUATIONS-Problems
  1. If y=y(x) is the solution of the differential equation ((2+sinx)/(y+1)...

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  2. The solution of tany(dy)/(dx)=sin(x+y)+sin(x-y) is

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  3. A family of curves has the differential equation xy(dy)/(dx)=2y^(2)-x^...

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  4. The solution of the differential equation (dy)/(dx)=sin(x+y)tan(x+y)-1...

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  5. The differential equation of the family y=ae^(x)+bxe^(x)+cx^(2)e^(x) o...

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

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  7. The solution of the differential equation (dy)/(dx)=(x-2y+1)/(2x-4y) i...

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  8. The solution of the differential equation (dy)/(dx)-ytanx=e^(x)secx is

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  9. The solution of the differential equation xy^(2)dy-(x^(3)+y^(3))dx=0 i...

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  10. The differential equation obtained by eliminating the arbitrary consta...

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  11. The solution (x+y+1)(dy)/(dx)=1 is

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  12. The solution of (dy)/(dx)=(y^(2))/(xy-x^(2)) is

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

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  14. The solution of (x^(2)+y^(2))dx=2xydy is

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  15. The solution of (1+x^(2))(dy)/(dx)+2xy-4x^(2)=0

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  16. The solution of (dx)/(dy)+(x)/(y)=-x^(2) is

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  17. If dx+dy=(x+y)(dx-dy), then log(x+y) is equal to

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  18. If x^(2)y-x^(3)(dy)/(dx)=y^(4)cosx then x^(3)y^(-3) is equal to

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  19. Which of the following statement is correct ? Statement I if dy+2xyd...

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  20. If (dy)/(dx)=(y+xtan.(y)/(x))/(x), then sin.(y)/(x) is equal to

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