Home
Class 12
MATHS
In (dy)/(dx),x is a independent variable...

In `(dy)/(dx),x` is a independent variable and `y` is the dependent variable. If independent and dependent variables are interchanged `(dy)/(dx)` becomes `(dy)/(dx)` and these two are connected by the relation `(dy)/(dx)dot(dx)/(dy)=1` . Find a relation between `(d^2y)/(dx^2)a n d(d^2y)/(dy^2)` .

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

In (dy)/(dx),x is a independent variable and y is the dependent variable. If independent and dependent variables are interchanged (dy)/(dx) becomes (dx)/(dy) and these two are connected by the relation (dy)/(dx)dot(dx)/(dy)=1 . Find a relation between (d^2y)/(dx^2)a n d(d^2x)/(dy^2) .

In (dy)/(dx),\ x is independent variable and y is the dependent variable. If independent and dependent variables are interchanged (dy)/(dx) becomes (dx)/(dy) and these two are connected by the relation (dy)/(dx)dot(dx)/(dy)=1 . Find a relation between (d^2y)/(dx^2) and (d^2x)/(dy^2)

Solve (d^2y)/(dx^2)=((dy)/(dx))^2

Solve (d^2y)/(dx^2)=((dy)/(dx))^2

Solve y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))

Find the order and degree of (d^2y)/dx^2+3(dy)/(dx)=ysin((d^2y)/dx^2)

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

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

Find order and degree: e^(dy/dx)=(1+(d^2y)/dx^2)

The solution of y^2=2y(dy)/(dx)-((dy)/(dx))^(2), is

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2) is n^2x (b) -n^2x (c) -n ...

    Text Solution

    |

  2. Find order & degree of equation xy ((d^2y)/dx^2)+x(dy/dx)^2-y(dy/dx)=0...

    Text Solution

    |

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

    Text Solution

    |

  4. If y^2=a^2cos^2x+b^2sin^2x ,t h e np rov et h a t(d^2y)/(dx^2)+y=(a^2b...

    Text Solution

    |

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

    Text Solution

    |

  6. If y=Acosn x+Bsinn x , show that (d^2y)/(dx^2)+n^2\ y=0 .

    Text Solution

    |

  7. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

    Text Solution

    |

  8. If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx...

    Text Solution

    |

  9. If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

    Text Solution

    |

  10. If y=tanx , prove that y2=2y y1 .

    Text Solution

    |

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

    Text Solution

    |

  12. If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

    Text Solution

    |

  13. If y^3-y=2x , prove that (d^2y)/(dx^2)=-(24 y)/((3y^2-1)^3) .

    Text Solution

    |

  14. If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

    Text Solution

    |

  15. If y=x^x , find (d^2y)/(dx^2) .

    Text Solution

    |

  16. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |