Home
Class 12
MATHS
If x=tan(1/alogy) , show that (1+x^2)(d^...

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

Text Solution

Verified by Experts

We have given
`x=tan(1/alogy)`
Take `tan^(−1)`on both sides,
`tan^(-1)x=1/alogy`
Differentiate w.r.t x,
`1/(x^2+1)=(1/ay^2)(dy)/(dx).........(1)`
Again differentiate w.r.t x
(∵ we need second order differential equation)
...
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 x=tan((1)/(a)log y), show that (1-x^(2))(d^(2)y)/(dx^(2))+(2x-a)(dy)/(dx)=0

If x=tan(1/alogy) , show that (1+x^(2))dy/dx=ay .

x(d^(2)y)/(dx^(2))+(dy)/(dx)+x=0

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

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

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

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

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

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

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

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y={x+sqrt(x^2+1)}^m , show that (x^2+1)y2+x y1-m^2\ y=0

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If y=asint and x=a(cost+logtant/2) , find (d^2y)/(dx^2) .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If (x-a)^2+(y-b)^2=c^2, for some c >0, p rov et h a t([1+((dy)/(dx))^...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Find second order derivative of sin(logx)

    Text Solution

    |

  18. Find second order derivative of log(sinx)

    Text Solution

    |

  19. Find second order derivative of e^xsin5x

    Text Solution

    |

  20. Find second order derivative of e^(6x)cos3x

    Text Solution

    |