Home
Class 12
MATHS
If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^...

If `y=(x+sqrt(1+x^2))^n` then `(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)`

A

`n^2 y `

B

`-n^(2) y `

C

`-y`

D

`2x^2 y `

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    DISHA PUBLICATION|Exercise Exercise-1 : Concept Builder (Topicwise)|60 Videos

  • DETERMINANTS

    DISHA PUBLICATION|Exercise EXERCISE -2 CONCEPT APPLICATOR|30 Videos

  • INTEGRALS

    DISHA PUBLICATION|Exercise EXERCISE-2 CONCEPT APPLICATOR|31 Videos

Similar Questions

Explore conceptually related problems

If y=(x+sqrt(1+x^(2)))^(n) then (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)

If y= sin (mlog (x+ sqrt( 1+x^(2)))),then (1+x^(2) ) (d^(2)y)/(dx^(2))+x(dy)/(dx) =

If y=[x+sqrt(x^(2)-1)]^(15)+[x-sqrt(x^(2)-1)]^(15) then (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx) is eqaul to

If y=(x+sqrt(1+x^(2)))^(n), then show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=n^(2)y

If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2=0 .

DISHA PUBLICATION-DIFFERENTIAL EQUATIONS -Exercise-2 : Concept Applicator
  1. A ray of light coming from origin after reflectiion at the point P (x ...

    Text Solution

    |

  2. The differential equation of the family of circles with fixed radius 5...

    Text Solution

    |

  3. If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

    Text Solution

    |

  4. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

    Text Solution

    |

  5. The solution of the differential equation (dy)/(dx)=(1-3y-3x)/(1+x+y) ...

    Text Solution

    |

  6. The solution of the equation (dy)/(dx)=((y^(2) -y-2))/(x^(2) + 2x+3) i...

    Text Solution

    |

  7. The solution of differential equation (dy)/(dx) = e^(x-y) + x^(2)e^(-y...

    Text Solution

    |

  8. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  9. Solution of the differential equation (1+e^(x/y))dx + e^(x/y)(1-x/y)dy...

    Text Solution

    |

  10. In a culture, the bacteria count is 1,00,000. The number is increas...

    Text Solution

    |

  11. The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2), is

    Text Solution

    |

  12. The solution of the differential equation x^(3)(dy)/(dx)+4x^(2) tany=e...

    Text Solution

    |

  13. Solution of the differential equation ((x+y-1)/(x+y-2))(dy)/(dx)=((x+y...

    Text Solution

    |

  14. Solve (1+e^((x)/(y)))dx + e^((x)/(y)) (1-(x)/(y))dy = 0

    Text Solution

    |

  15. The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (...

    Text Solution

    |

  16. v34

    Text Solution

    |

  17. Solve: dy/dx=(y f\'(x)-y^2)/f(x), where f(x) is a given function of x

    Text Solution

    |

  18. The solution of the differential equation (x+y)^(2)(dy)/(dx) = a^(2...

    Text Solution

    |

  19. The particular solution of the differential equation sin^(-1)((d^2 y)/...

    Text Solution

    |

  20. Solution of differential equation (x^(2) -2x + 2y^(2)) dx + 2xy dy = ...

    Text Solution

    |