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Assertion (A) : The differential equaito...

Assertion (A) : The differential equaiton of the family of rectangular hyperbolas which have the coordinate axes as asymptotes is `xy_(1) + y = 0`
Reason (R) : The number of arbitrary constants in the general solution of differential equation is equal to the order of the differential equation.
Then the statement among the following is

A

Both (A) and (R) are true and R is correct explanation of A

B

Both (A) and (R) are true and R is not correct explanation of A

C

A is true, (R) is false

D

(A) is false (R) is true

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The correct Answer is:
A
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AAKASH SERIES-DIFFERENTIAL EQUATIONS-Exercise - II
  1. If the solution of cosec^(2)x(dy)/(dx) - (1)/(y) = 0 is ax + b sin 2x ...

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  2. Assertion (A) : Integrating factor of 1+(x tan y - sec)(dy)/(dx) = 0 i...

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  3. Assertion (A) : The differential equaiton of the family of rectangular...

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  4. Asserton (A) : The solution of (dy)/(dx) = (x+y)/(x) is e^(y//x) = cx ...

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  5. The solution of the differential equation (dy)/(dx) - 2y tan 2x = e^(x...

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  6. An integrating factor of the equation (1+y+x^(2)y)dx+(x+x^(3))dy=0 is

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

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  8. The differential equation of co-axial system of circles x^(2) + y^(2) ...

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  9. The trajectories orthogonal to x^(2)+y^(2) = 2ax is

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  10. The volume of spherical ballon being inflated changes at a constant ra...

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  11. In a bank, principal increases continuously at the rate of r% per yeat...

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  12. In a bank, principal increases continuously at the rate of 5% per yea...

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  13. In a culture, the bacteria count is 1,00,000. The number is increased ...

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  14. The population of a village increases continuously at the rate proport...

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

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  16. If y = y (x) is the solution of the differential equation ((2 + sin x)...

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  17. (dy)/(dx) +2x tan(x-y) = 1 rArr sin(x-y) =

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  18. Integrating factor of the differential equation (1-x^(2)) (dy)/(dx) + ...

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  19. The differential equation (dy)/(dx) = (1)/(ax + by + c) where a,b,c a...

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

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