Home
Class 12
MATHS
If y(t) is a solution of (1+t)(dy)/(dt)...

If `y(t)` is a solution of `(1+t)(dy)/(dt)-t y=1a n dy(0)=-1` then show that `y(1)=-1/2dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

Similar Questions

Explore conceptually related problems

If y(t) is a solution of (1+t)dy/dt-t y=1 and y(0)=-1 then y(1) is

The solution of (dy)/(dx)-y=1, y(0)=1 is given by

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

If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x-y)

x=a(t-sin t),y=a(1+cos t) then (dy)/(dx) =

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

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

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

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

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

RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Solve each of the following initial value problems sqrt(1-y^2)dx=...

    Text Solution

    |

  2. Solve the following differential equations: x(dy)/(dx)+y=x e^x

    Text Solution

    |

  3. If y(t) is a solution of (1+t)(dy)/(dt)-t y=1a n dy(0)=-1 then show ...

    Text Solution

    |

  4. Solve: (x+2y^3)dy=ydxdot

    Text Solution

    |

  5. Solve each of the following initial value problems: x(dy)/(dx...

    Text Solution

    |

  6. Solve each of the following initial value problems: (dy)/(dx)+(2x)/(...

    Text Solution

    |

  7. Solve the following differential equations: (2x-10 y^3)(dy)/(dx)+y=0

    Text Solution

    |

  8. Solve the following differential equations: (dy)/(dx)+y cotx=x^2cotx+2...

    Text Solution

    |

  9. Solve the following differential equations: (dy)/(dx)+ycosx=sinxcosx

    Text Solution

    |

  10. Solve the following differential equations: (x+tany)dy=sin2ydx

    Text Solution

    |

  11. Solve the following differential equations: (dy)/(dx)-y= xe^x

    Text Solution

    |

  12. Solve the following differential equations: (1+x^2)(dy)/(dx)-2x y=(x^2...

    Text Solution

    |

  13. The surface are of a balloon being inflated changes at a constant r...

    Text Solution

    |

  14. Solve the following differential equations: (dy)/(dx)+2y=x e^(4x)

    Text Solution

    |

  15. Suppose the growth of a population is proportional the umber presen...

    Text Solution

    |

  16. A population grows at the rate of 8% per year. How long does it tak...

    Text Solution

    |

  17. Verify that y=log(x+sqrt(x^2+a^2))^2 satisfies the differential equa...

    Text Solution

    |

  18. Verify that y=c e^(t a n-1x) is a solution of differential equatio...

    Text Solution

    |

  19. Show that the differential equation of which y=2(x^2-1)+c e^-(x^2) is ...

    Text Solution

    |

  20. Form the differential equation corresponding to y^2-2a y+x^2=a^2 by el...

    Text Solution

    |