Home
Class 12
MATHS
If y=sin^(-1)x , then show that (1-x^2)\...

If `y=sin^(-1)x` , then show that `(1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0` .

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|406 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

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

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

If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^(-1)x), show that ((1-x^2)d^(2y))/(dx^2)=x(dy)/(dx)-4y

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

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

If y=e^m\ sin^((-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0 .

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

If y=(sin^(-1)x)/(sqrt(1-x^2)) , show that (1-x^2)(d^2y)/(dx^2)-3x(dy)/(dx)-y=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

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

  2. If y=log{x+ sqrt( x^2+a^2 )} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy...

    Text Solution

    |

  3. If y=sin^(-1)x , then show that (1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0 .

    Text Solution

    |

  4. If y=e^m\ sin^((-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2...

    Text Solution

    |

  5. If y={x+sqrt(x^2+1)}^m , show that (x^2+1)y2+x y1-m^2\ y=0

    Text Solution

    |

  6. If y=(sin^(-1)x)/(sqrt(1-x^2)) , show that (1-x^2)(d^2y)/(dx^2)-3x(dy)...

    Text Solution

    |

  7. If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

    Text Solution

    |

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

    Text Solution

    |

  9. Find (d^2y)/(dx^2) , if x=a t^2,\ \ y=2a t .

    Text Solution

    |

  10. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

    Text Solution

    |

  11. If x=asint and y=a(cost+log tan(t/2) ) , find (d^2y)/(dx^2) .

    Text Solution

    |

  12. lf x=acostheta+bsintheta, y=asintheta-bcostheta then show that y^2(d^...

    Text Solution

    |

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

    Text Solution

    |

  14. If x=sintheta , y=cosptheta , prove that (1-x^2)y2-x y1+p^2y=0 , where...

    Text Solution

    |

  15. If (x-a)^2+(y-b)^2=c^2, for some c >0, prove that([1+((dy)/(dx))^2]^(...

    Text Solution

    |

  16. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

    Text Solution

    |

  17. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  18. In (dy)/(dx),\ x is independent variable and y is the dependent ...

    Text Solution

    |

  19. In (dy)/(dx),x is a independent variable and y is the dependent vari...

    Text Solution

    |

  20. Find second order derivative of x^3+tanx

    Text Solution

    |