Home
Class 12
MATHS
Verify that the function y= a cos x+b si...

Verify that the function `y= a cos x+b sin x`, where `a, b in R` is a solution of the differential equation `(d^(2)y)/(dx^2)+y=0`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (SHORT ANSWER TYPE QUESTIONS)|11 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANSWER TYPE QUESTIONS)|21 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT PUBLICATION|Exercise ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 11C)|15 Videos
  • DETERMINANTS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE |39 Videos
  • INTEGRATION

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (6 MARK)|4 Videos
ARIHANT PUBLICATION-DIFFERENTIAL EQUATION-CHAPTER PRACTICE (VERY SHORT ANSWER TYPE QUESTIONS)
  1. Find the order and degree of the following differential equations : ...

    Text Solution

    |

  2. State whether y= e^(-x)(x+a) is a solution of differential equation (d...

    Text Solution

    |

  3. Verify that the function y= a cos x+b sin x, where a, b in R is a solu...

    Text Solution

    |

  4. Show that the function y=(A+Bx)e^(3x) is a solution of the equation (d...

    Text Solution

    |

  5. Show that y= Cx+(a)/(C ) is a solution of differential equation y= x(d...

    Text Solution

    |

  6. Prove that xy= ae^(x)+be^(-x)+x^(2) is the general solution of the dif...

    Text Solution

    |

  7. Show that the function phi, defined by phi(x)= cos x(x in R), satisfie...

    Text Solution

    |

  8. Find the differential equation of the family of all straight lines.

    Text Solution

    |

  9. Write the differential equation of all non-horizontal lines in a plane...

    Text Solution

    |

  10. Write the differential equation representing the family of curves y= m...

    Text Solution

    |

  11. Find the differential equation of the family of concentric circles hav...

    Text Solution

    |

  12. Find the differential equation of the family of curves y= Ae^(x)+Be^(-...

    Text Solution

    |

  13. Form the differential equation by aliminating A and B in Ax^(2)+By^(2)...

    Text Solution

    |

  14. Find the differential equation corresponding to curve y= a cos (x+b), ...

    Text Solution

    |

  15. Solve the following differential equations : (dy)/(dx)= sqrt(1-y^2),...

    Text Solution

    |

  16. Solve the following differential equations : (dy)/(dx)+y=1, y ne 1.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Write the solution of differential equation (e^(x)+e^(-x))dy= (e^(x)-e...

    Text Solution

    |

  20. If (dy)/(dx)=ye^(x)" and "x=0, y= e, then find the value of y, when x=...

    Text Solution

    |