Home
Class 12
MATHS
If y=e^(acos^(-1)x),-1lt=x<1, show that ...

If `y=e^(acos^(-1)x),-1lt=x<1`, show that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 2019

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise Section D|2 Videos

Similar Questions

Explore conceptually related problems

If y=e^(a cos^(-1)x)\ ,\ -1\ lt=xlt=1, show that (1-x^2)(d^2y)/(dx^2)-\ x(dy)/(dx)-\ a^2y=0

If y=e^{a\cos ^{-1}x},-1lt=xlt=1, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0 .

If y=e^(asin^(-1)x)\ ,\ -1\ lt=x\ lt=1, then show that (1-x^2)\ (d^2\ y)/(dx^2)-\ x(dy)/(dx)-\ a^2y=0

Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x lt 1

Given f(x)={(x^2 xx e^(2(x-1)), 0 le x le 1), (acos(2x-2)+bx^2, 1 lt x le2):} is differentiable at x=1 , then the value of |a - b| is

Form the differential equation having y=(sin^(-1)x)^2+Acos^(-1)x+B ,w h e r eAa n dB are arbitrary constants, as its general solution.

If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) is equal to (a) 1/(2(1+x^2)),x in R (b) 1/(2(1+x^2)),x >0 (c) (-1)/(2(1+x^2)),x<0 (d) 1/(2(1+x^2)),x<0

If y = 2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))) , then "………"lt y lt "………" .

y = cos ^(-1)((2x)/(1 +x^(2))),-1 lt x lt1 . find dy/dx

Draw the graph of y=|x|^(1/2) for -1lt=x<1.

XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Solve the following differential equation: (1+ e ^(y/x)) dy + e^(y...

    Text Solution

    |

  2. Find f'(x) if f(x) = tan x^(tan x)

    Text Solution

    |

  3. If y=e^(acos^(-1)x),-1lt=x<1, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(d...

    Text Solution

    |

  4. If f(x) = sqrt ((sec x -1)/(sec x + 1)) , find f'( pi /3)

    Text Solution

    |

  5. The area of the triangle formed by the vertices O, A, and B, where vec...

    Text Solution

    |

  6. If A = [(5, -1, 4), (2, 3, 5), (5, -2, 6)] , find A^(-1) and use it t...

    Text Solution

    |

  7. The vectors 3hati - hatj +2hatk, 2hati+hatj+3hatk and hati+lambdahatj-...

    Text Solution

    |

  8. A cottage industry manufactures pedestal lamps and wooden shades.Both ...

    Text Solution

    |

  9. If x, y, z are different and Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[...

    Text Solution

    |

  10. Find the area of the triangle formed by O ,A ,B when vec O A= hat ...

    Text Solution

    |

  11. Prove that tan^-1(1/4)+ tan^-1(2/9) = 1/2sin^-1(4/5)

    Text Solution

    |

  12. Check whether the relation R in the set N of natural numbers given by ...

    Text Solution

    |

  13. The function f(x) : (x-1)/(x( x^(2) -1)) is discontinuous at (a) exa...

    Text Solution

    |

  14. The Integrating Factor of the differential equation x(dy)/(dx)-y=2x^2...

    Text Solution

    |

  15. If I vec(a)I = 4 and -3 le lamda le 2,then Ilambda vec(a)I lies in ...

    Text Solution

    |

  16. Differentiate sec^2 (x^2) with respect to x^2

    Text Solution

    |

  17. If cos (sin^(-1)(2/sqrt(5)) + cos^(-1)x) = 0, then x is equal to A) ...

    Text Solution

    |

  18. Evaluate : int(-pi/2)^(pi/2)xcos^2 xdx

    Text Solution

    |

  19. The relation R in the set {1,2,3} given by R = {(1,2), (2,1),(1,1)} is...

    Text Solution

    |

  20. The function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both...

    Text Solution

    |