Home
Class 12
MATHS
Let y(x) be the solution the differentia...

Let y(x) be the solution the differential equation `(xlogx)(dy)/(dx)+y=2xlogx,(xge1).` Then y€ is equal to

A

e

B

0

C

2

D

2e

Text Solution

Verified by Experts

The correct Answer is:
C
We have `(dy)/(dx) + y/(xlogx)=2`
`I.F. = e^(int1/(xlogx)dx)=e^(log(logx))=logx`
Now solution, is
`y(logx)=int2(logx)dx`
`rArr y(logx)=2[xlogx-x]+c`
When x=1, c=2.
When `x=e` then
`y=2(e-e)+2`
or y=2
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)+y=2xlogx, (x ge1) Then y(e) is equal to-

The solution of the differential equation (dy)/(dx)=e^(2x+y) is

The solution of the differential equation (dy)/(dx)=e^(x+y) is

The solution of the differential equation (x+2y^3)((dy)/(dx))=y is

The solution of the differential equation (dy)/(dx)=e^(x-y)+1 is

The solution of the differential equation (dy)/(dx)+P(x)y=0 is -

The solution of the differential equation (x+2y^(3))(dy)/(dx)=y is -

The solution of the differential equation (dy)/(dx)=(x-y)/(x+y) is -

Solve the differential equation : (dy)/(dx)-y/x=2x^2

The solution of the differential equation (x+y)(dx-dy)=dx+dy is -

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. At present, a firm is manufacturing 2000 items. It is estimated tha...

    Text Solution

    |

  2. Let the population of rabbits surviving at a time t be governed by t...

    Text Solution

    |

  3. Let y(x) be the solution the differential equation (xlogx)(dy)/(dx)+y=...

    Text Solution

    |

  4. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

    Text Solution

    |

  5. If (2+sinx)(dy)/(dx)+(y+1)cosx=0 and y(0)=1, then y((pi)/(2)) is equal...

    Text Solution

    |

  6. Let y=g(x) be the solution of the differential equation sin (dy)/(dx...

    Text Solution

    |

  7. A curve passes through the point (1,pi/6) . Let the slope of the curve...

    Text Solution

    |

  8. The function y=f(x) is the solution of the differential equation (d...

    Text Solution

    |

  9. If y=y(x) satisfies the differential equation 8sqrt(x)(sqrt(9+sqrt(x))...

    Text Solution

    |

  10. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

    Text Solution

    |

  11. Consider the family of all circles whose centers lie on the straigh...

    Text Solution

    |

  12. Let y(x) be a solution of the differential equation (1+e^x)y^(prime...

    Text Solution

    |

  13. A solution curve of the differential equation (x^(2)+xy+4x+2y+4)(dy)/(...

    Text Solution

    |

  14. Let f: R->R and g: R->R be two non-constant differentiable functions. ...

    Text Solution

    |

  15. Let f be a real-valued differentiable function on R (the set of ...

    Text Solution

    |

  16. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  17. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

    Text Solution

    |

  18. Let f:R to R be a differentiable function with f(0)=0. If y=f(x) satis...

    Text Solution

    |

  19. The order of the differential equation whose general solution is y = c...

    Text Solution

    |

  20. Order of the differential equation whose general solution is y = (ax)/...

    Text Solution

    |