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The differential equation representing the family of curve `y = A sin ( x+ B) ` where A and B are parametres is :

A

`y'' - y = 0 `

B

`(d^(2)x)/(dy^(2))=1`

C

`y'' = 0 `

D

`y'' + y = 0 `

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The correct Answer is:
D
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PREMIERS PUBLISHERS-ORDINARY DIFFERENTIAL EQUATIONS -PROBLEMS FOR PRACTICE (Choose the Correct Answer)
  1. The order and degree of the differential equation y'' (y - (y')^(3))...

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  2. The degree of the differential equation rho= (1+((dy)/(dx))^(2))^(3/2...

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  3. The order and degree of the differential equation ((dy)/(dx))^(2) = ...

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  4. The solution of the equation (dx)/(dy) + Px = Q where P and Q are func...

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  5. The degree of the differential equation (d^(2)y)/(dx^(2)) x = sqrt(y +...

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  6. If y^(2) = 4ax where a is constant then the differential equation for...

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  7. The differential equation formed if y = (A - Bx ) e^(-2x) is :

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  8. The differential equation that will represent the family of all circle...

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  9. Solve (x^(2)-y) dx+(y^(2)-x)dy=0 , if it passes through origin :

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  10. The differential equation representing the family of curve y = A sin ...

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  11. The order and degree of the differential equation sin^(3)x (dx + dy)...

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  12. The general solution of (dy)/(dx) + y/x = 0 is :

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  13. If I.F of (dy)/(dx) +P(x)y = Q (x) is cos^(2)x then P (x) =

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  14. The solution of (dy)/(dx)+1/(x^(2)+1)= 0 is

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

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  16. If sin^(3)x is the integrating factor of the differential equation (dy...

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  17. The number of arbitrary constant in the particular solution of a diff...

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  18. The slope at any point of the curve y = f(x) is given by (dy)/(dx)= 2x...

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  19. The degree of the differential equation ((d^(2)y)/(dx^(2)))^(2) = sqrt...

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

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