Home
Class 12
MATHS
If y=(cot^(-1)x)^2,p rov et h a ty2(x^2...

If `y=(cot^(-1)x)^2,p rov et h a ty_2(x^2+1)^2+2x(x^2+1)y_1=2.`

Text Solution

Verified by Experts

Here,

`y=(cot ^{-1} x)^{2}`

Differentiating `w, r, t, x`, we get

...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If y=(cot^(-1)x)^(2), prove that y_(2)(x^(2)+1)^(2)+2x(x^(2)+1)y_(1)=2

If y=(tan^(-1)x)^2 , show that (x^2+1)^2y_2+2x(x^2+1)y_1=2 .

If y = (cot^(-1) x)^(2) then

If y=(tan^(-1)x)^(2) show that (x^(2)+1)^(2)y_(2)+2x(x^(2)+1)y_(1)=2

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

If y=(tan^(-1)x)^(2), then prove that (1+x^(2))^(2)y_(2)+2x(1+x^(2))y_(1)=2

y=(cot^(-1)x)^(2), thenshowthat (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)

If y=(x^(2)+x+1)/(x^(2)-x+1)," then "(x^(2)-x+1)^(2)y_(1)=

If y=log(sqrt(x)+(1)/(sqrt(x)))^(2), then , x(x+1)^(2)y_(2)+(x+1)^(2)y_(1) is

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...

    Text Solution

    |

  2. If x=a(cost+tsint) and y=a(sint-tcost), then find the value of (d^2y)...

    Text Solution

    |

  3. If y=(cot^(-1)x)^2,p rov et h a ty2(x^2+1)^2+2x(x^2+1)y1=2.

    Text Solution

    |

  4. If y=e^xcosx ,p rov et h a t(d^2y)/(dx^2)=2e^xcos(x+pi/2)dot

    Text Solution

    |

  5. If x=cos t + (log tant)/2, y=sin t, then find the value of (d^2y)/(dt^...

    Text Solution

    |

  6. Find A and B so that y=Asin3x+bcos3x satisfies the equation (d^2y)/(d...

    Text Solution

    |

  7. If x=asint-bcost ,y=acost+bsint ,"p r o v et h a t" (d^2y)/(dx^2)=-...

    Text Solution

    |

  8. If y=e^(2x) (ax+b), show that y2-4y1+4y=0

    Text Solution

    |

  9. If x=asectheta,y=btantheta,"p r o v et h a t"(d^2y)/(dx^2)=-(b^4)/(a...

    Text Solution

    |

  10. If y=e^"tan"^((-1)"x"), prove that (1+x^2)y2+(2x-1)y1=0.

    Text Solution

    |

  11. If y=(sin^(-1)x)^2 ,prove that (1-x^2)y2-x y1-2=0.

    Text Solution

    |

  12. If y="log"(x+sqrt(x^2+1)),"show that"(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=...

    Text Solution

    |

  13. If x=sin(1/alogy),"s h o wt h a t"(1-x^2)y2-xy1-a^2y=0.

    Text Solution

    |

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

    Text Solution

    |

  15. If y=e^-x cos x, show that (d^2y)/(dx^2)= 2e^-1 sin x

    Text Solution

    |

  16. If y=log(sinx),"p r o v et h a t"(d^3y)/(dx^3)=2cosxcos e c^3xdot

    Text Solution

    |

  17. If y=x^3logx ,"p r o v et h a t"(d^4y)/(dx^4)=6/xdot

    Text Solution

    |

  18. If y=(logx)/x ,s howt h a t(d^2y)/(dx^2)=(2logx-3)/(x^3)

    Text Solution

    |

  19. If y=2 sin x+3cos x, show that (d^2y)/(dx^2)+y=0

    Text Solution

    |

  20. Find . (d^2y)/(dx^2),ifx=a t^2,y=2a tdot

    Text Solution

    |