Home
Class 12
MATHS
if x=(1+lnt)/t^2 and y=(3+2lnt)/t then s...

if `x=(1+lnt)/t^2` and `y=(3+2lnt)/t` then show that `y(dy)/(dx)=2x((dy)/(dx))^2+1`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exercise 10H|10 Videos

  • DIFFERENTIAL EQUATIONS WITH VARIABLE SEPARABLE

    RS AGGARWAL|Exercise Exercise 19B|60 Videos

  • FUNCTIONS

    RS AGGARWAL|Exercise Exercise 2D|11 Videos

Similar Questions

Explore conceptually related problems

if x=(1+ln t)/(t^(2)) and y=(3+2ln t)/(t) then show that y(dy)/(dx)=2x((dy)/(dx))^(2)+1

(y-x(dy)/(dx))=3(1-x^(2)(dy)/(dx))

If x=a^(sqrt(sin-1)t) and y=a^(sqrt(cos-1)t), then show that (dy)/(dx)=-(y)/(x)

(dy)/(dx)=(x+y+1)/(2x+2y+3)

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

If x=(1-t^2)/(1+t^2) and y=(2at)/(1+t^2) , then (dy)/(dx)=

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

A function is reprersented parametrically by the equations x=(1+t)/(t^(3));y=(3)/(2t^(2))+(2)/(t). Then the value of |(dy)/(dx)-x((dy)/(dx))

RS AGGARWAL-DIFFERENTIATION-Exercise 10I
  1. Find (dy)/(dx), when x=cos^(-1)1/(sqrt(1+t^2))"and"y=sin^(-1)t/(sqrt(1...

    Text Solution

    |

  2. "If "x=3cost-2cos^(3)t,y=3sint-2sin^(3)t," show that"(dy)/(dx)=cott.

    Text Solution

    |

  3. if x=(1+lnt)/t^2 and y=(3+2lnt)/t then show that y(dy)/(dx)=2x((dy)/(d...

    Text Solution

    |

  4. Find (dy)/(dx) , when x=a(1-costheta) and y=a(theta+sintheta) at theta...

    Text Solution

    |

  5. If x=2costheta-cos2\ theta and y=2sintheta-sin2\ theta , prove that (d...

    Text Solution

    |

  6. If x=sin^3t/(sqrtcos2t), y=cos^3t/sqrt(cos2t) show that dy/dx =0 at t=...

    Text Solution

    |

  7. "If "x=(2costheta-cos 2theta)and y=(2sin theta-sin 2theta)," find "((d...

    Text Solution

    |

  8. If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)

    Text Solution

    |

  9. Find the second derivative of : (i)x^(11)" "(ii)5^(x)" "(ii...

    Text Solution

    |

  10. Find the second derivative of: (i)x sin x" "(ii)e^(2x)cos 3x" ...

    Text Solution

    |

  11. If y=x+tanx , show that cos^2x\ (d^2y)/(dx^2)-2y+2x=0 .

    Text Solution

    |

  12. If y=2sinx+3cosx ,show that (d^2y)/(dx^2)+y=0

    Text Solution

    |

  13. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

    Text Solution

    |

  14. If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.

    Text Solution

    |

  15. If y=sec x-tanx,show that (cosx)(d^(2)y)/(dx^(2))=y^(2).

    Text Solution

    |

  16. If y=("cosec "x+cotx), prove that (sinx)(d^(2)y)/(dx^(2))-y^(2)=0.

    Text Solution

    |

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

    Text Solution

    |

  18. If y=sin(sinx) then prove that (d^2y)/(dx^2)+tanx. (dy)/(dx)+y cos^2...

    Text Solution

    |

  19. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

    Text Solution

    |

  20. Find the second derivative of e^(3x)sin4x.

    Text Solution

    |