Home
Class 12
MATHS
If y=x^x , prove that (d^2y)/(dx^2)-1/y(...

If `y=x^x ,` prove that `(d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • EXAM REVISION SERIES

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise All Questions|19 Videos

Similar Questions

Explore conceptually related problems

If y=x^(x) , prove that: (d^(2)y)/(dx^(2))-1/y((dy)/(dx))^(2) - y/x=0

If y=e^x(sin x+cosx) prove that (d^2y)/(dx^2)-2 (dy)/(dx)+2y=0 .

If y=e^x(sinx+cosx) prove that (d^2y)/(dx^2)-2(dy)/(dx)+2y=0 .

If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

If x y=1 , prove that (dy)/(dx)+y^2=0 .

If y=x/(x+2) , prove that x(dy)/(dx)=(1-y)y

If x=sint ,y=sinpt , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

If y= cot x, prove that (d^(2)y)/(dx^(2)) + 2y (dy)/(dx)= 0.

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the position vector of a point which divides the join of points w...

    Text Solution

    |

  2. Matrix A=[0 2b-2 3 1 3 3a3-1] is given to be symmetric, find values of...

    Text Solution

    |

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

    Text Solution

    |

  4. Show that the equation of normal at any point t on the curve x=3cost-c...

    Text Solution

    |

  5. If A is a square matrix such that A^2=I , then find the simplified val...

    Text Solution

    |

  6. Find the maximum value of |[1, 1, 1],[ 1, 1+sintheta,1],[ 1, 1, 1+cost...

    Text Solution

    |

  7. Find the vector equation of a plane which is at a distance of 5 units ...

    Text Solution

    |

  8. Find : int(sqrt(x))/(sqrt(a^3-x^3))dxdot

    Text Solution

    |

  9. Find the intervals in which f(x) = sin 3x – Cos 3x, 0 < x < pi, is str...

    Text Solution

    |

  10. Show that the altitude of the right circular cone of maximum volume th...

    Text Solution

    |

  11. A and B throw a pair of dice alternately. A wins the game if he gets a...

    Text Solution

    |

  12. Prove that |[yz-x^2,zx-y^2,xy-z^2],[zx-y^2,xy-z^2,yz-x^2],[xy-z^2,yz-x...

    Text Solution

    |

  13. Using elementary transformations, find the inverse of the matrix A = [...

    Text Solution

    |

  14. Three persons A, B and C apply for a job of Manager in a Private Compa...

    Text Solution

    |

  15. Solve for : 2\ tan^(-1)(cosx)=tan^(-1)(2\ cos e c\ x) .

    Text Solution

    |

  16. int(-1)^2|x^3-x|dxdot

    Text Solution

    |

  17. Find the particular solution of the differential equation (1-y^2)(1+lo...

    Text Solution

    |

  18. Find the general solution of the differential equation (1+y^(2))+(x-e^...

    Text Solution

    |

  19. Show that the vectors vec a , vec b and vec c are coplanar if vec a+...

    Text Solution

    |

  20. Find the vector and Cartesian equations of the line through the point ...

    Text Solution

    |