Home
Class 12
MATHS
Show that the differential equation x co...

Show that the differential equation `x cos ((y)/(x))(dy)/(dx) = y cos ((y)/(x)) + x` is homogeneous and solve it.

Text Solution

Verified by Experts

The correct Answer is:
`sin ((y)/(x)) = log |Cx|`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXAMPLES|5 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT BANGLISH|Exercise EXERCISE - 9.1|12 Videos

  • DETERMINANTS

    NCERT BANGLISH|Exercise Miscellaneous Exercises on Chapter 4|18 Videos

  • INTEGRALS

    NCERT BANGLISH|Exercise EXERCISE 7.12|44 Videos

Similar Questions

Explore conceptually related problems

Show that the differential equation 2ye^(x)/(y) dx + ( y - 2xe^(x)/(y)) dy = 0 is homogeneous and find its particular solution, given that, x = 0 when y = 1.

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

The I.F of the differential equation (dy)/(dx)+(3)/(x)y=3 cos x is

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

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

solve x(dy)/(dx) - y + x sin ((y)/(x)) = 0

Show that the differential equation (x - y) (dy)/(dx) = x + 2y is homogeneous and solved it.

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

Solve the differential equation (x)dy = ( 1 + y^(2))dx .

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

NCERT BANGLISH-DIFFERENTIAL EQUATIONS-MISCELLANEOUS EXERCISE
  1. Show that the differential equation x cos ((y)/(x))(dy)/(dx) = y cos (...

    Text Solution

    |

  2. For each of the differential equations given below, indicate its order...

    Text Solution

    |

  3. show that if. y = sin 3x : then(d^(2)y)/(dx^(2)) + 9y = 0

    Text Solution

    |

  4. Form the differential equation representing the family of curves give...

    Text Solution

    |

  5. Prove the x^(2) - y^(2) = c (x^(2) + y^(2))^(2) is the general solutio...

    Text Solution

    |

  6. Form the differential equation of the family of circles in the first q...

    Text Solution

    |

  7. Find the general solution of the differential equation (dy)/(dx) + sqr...

    Text Solution

    |

  8. Show that the general solution of the differential equation (dy)/(dx) ...

    Text Solution

    |

  9. Find the equation of the curve passing through the point (0, (pi)/(4))...

    Text Solution

    |

  10. Find the particular solution of the differential equation (1 + e^(2x)...

    Text Solution

    |

  11. Solve the differential equation y dx = (x + y^(2))dy ( y ne 0).

    Text Solution

    |

  12. Find a particular solution of the differential equation (x - y)(dx + d...

    Text Solution

    |

  13. Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](...

    Text Solution

    |

  14. Find a particular solution of the differential equation (dy)/(dx) + y...

    Text Solution

    |

  15. Find a particular solution of the differential equation (x + 1)(dy)/(d...

    Text Solution

    |

  16. The population of a village increases continuously at the rate propor...

    Text Solution

    |

  17. The general solution of the differential equation (y dx - x dy)/(y ) =...

    Text Solution

    |

  18. The general solution of a differential equation of the type (dy)/(dx)...

    Text Solution

    |

  19. The general solution of the differential equation e^(x) dy + (y e^(x) ...

    Text Solution

    |