Home
Class 12
MATHS
If logy=tan^(-1)x , show that (1+x^2)y2+...

If `logy=tan^(-1)x` , show that `(1+x^2)y_2+(2x-1)y_1=0` .

Text Solution

AI Generated Solution

To solve the problem, we need to show that if \( \log y = \tan^{-1} x \), then \[ (1+x^2)y'' + (2x-1)y' = 0 \] where \( y' \) is the first derivative of \( y \) with respect to \( x \) and \( y'' \) is the second derivative. ...
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 logy=tan^(-1)x,"then "(1+x^(2))y_(2)+(2x-1)y_(1)+4=

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

If y=e^(tan^(-1)x), prove that (1+x^(2))y_(2)+(2x-1)y_(1)=0

If y=e^(tan^^)((-1)x), prove that (1+x^(2))y_(2)+(2x-1)y_(1)=0

" 1(a) If "y=e^(a sin^(-1)x)" ,show that "(1-x^(2))y_(2)-xy_(1)-a^(2)y=0

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

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

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

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

y = e ^ (xx) x tan ^ (- 1) x, showthat (1 + x ^ (2)) y_ (2) -2 (1-x + x ^ (2)) y_ (1) + (1 -x ^ (2)) y = 0

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=e^(2x)(a x+b) , show that y2-4\ y1+4\ y=0 .

    Text Solution

    |

  2. If x=sin(1/alogy) , show that (1-x^2)y2-x\ y1-a^2\ y=0 .

    Text Solution

    |

  3. If logy=tan^(-1)x , show that (1+x^2)y2+(2x-1)y1=0 .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If y=(tan^(-1)x)^2 , then prove that (1+x^2)^2\ y2+2x\ (1+x^2)y1=2 .

    Text Solution

    |

  7. If y=cotx show that (d^2y)/(dx^2)+2y(dy)/(dx)=0 .

    Text Solution

    |

  8. Find (d^2y)/(dx^2) , where y=log((x^2)/(e^2)) .

    Text Solution

    |

  9. If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

    Text Solution

    |

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

    Text Solution

    |

  11. If y=cos^(-1)x , find (d^2y)/(dx^2) in terms of y alone.

    Text Solution

    |

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

    Text Solution

    |

  13. If y=500\ e^(7x)+600\ e^(-7x) , show that (d^2y)/(dx^2)=49\ y .

    Text Solution

    |

  14. If x=2cost-cos2t ,\ \ y=2sint-sin2t , find (d^2y)/(dx^2) at t=pi/2 .

    Text Solution

    |

  15. If x=4z^2+5,\ \ y=6z^2+7z+3, find (d^2y)/(dx^2) .

    Text Solution

    |

  16. If y=log(1+cosx) , prove that (d^3y)/(dx^3)+(d^2y)/(dx^2)dot(dy)/(dx)=...

    Text Solution

    |

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

    Text Solution

    |

  18. If y=3\ e^(2x)+2\ e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

    Text Solution

    |

  19. If y=(cot^(-1)x)^2 , prove that y2(x^2+1)^2+2x(x^2+1)y1=2 .

    Text Solution

    |

  20. If y=cosec^(-1)x ,\ \ x >1 , then show that x(x^2-1)(d^2y)/(dx^2)+(2x^...

    Text Solution

    |