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The solution of (dy)/(dx) = (xy)/(x^(2) ...

The solution of `(dy)/(dx) = (xy)/(x^(2) + y^(2))` is

A

`x = ce^((x^(2))/(y^(2)))`

B

`y = ce^((x^(2))/(y^(2)))`

C

`x = ce^((x^(2))/(2y^(2)))`

D

`x = ce^((2x^(2))/(y^(2)))`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-DIFFERENTIAL EQUATIONS-Practice Exercise
  1. Solve : x dy= (y+x " cos"^(2)(y)/(x))dx

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  2. Solve : x " sin"(y)/(x).(dy)/(dx)=y " sin"(y)/(x)-x

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

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

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  5. The substitution required to change equation (dy)/(dx) = (2x+3y+5)/(4x...

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  6. To change (3x+4y+5) - (2x+3y+4)(dy)/(dx) = 0 into homogeneous equation...

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  7. The solution of (dy)/(dx) = (x-2y + 3)/(2x-y + 5) is

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  8. The integrating factor of the differential equation (dy)/(dx) (x log x...

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  9. An equation (dy)/(dx) + p(x).y = q(x) is called

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  10. The solution of (1+x^(2)) (dy)/(dx) + y = e^(Tan^(-1)x) is

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  11. The integrating factor of c Cos x((dy)/(dx)) + (x Sin x + Cos x)y =...

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  12. The solution of 2x(dy)/(dx) + y = 2x^(3) is

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  13. The solution of (dy)/(dx) + (xy)/(1 + x^(2)) = (1)/(x (1 + x^(2))) is

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  14. The solution of (dy)/(dx) -y tan x = e^(x) sec x is

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  15. The solution of (dy)/(dx) + (3x^(2) y)/(1 + x^(3)) = (1+ x^(2))/(1 + x...

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  16. The solution of x log x (dy)/(dx) +y =1 is

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  17. The solution of y^(2) dx + (3xy -1) dy = 0 is

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  18. The solution of dx + x dy = e^(-y) sec^(2) y dy is

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  19. The solution of sec x(dy)/(dx) = y + sin x is

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  20. The solution of (dy)/(dx) + (3)/(x) y = (1)/(x^(2)), at y=2, x=1

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