Home
Class 12
MATHS
If y = 2 sin x + 3 cos x, prove that y +...

If y = 2 sin x + 3 cos x, prove that `y + (d^2y)/(dx^2) = 0`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • APPLICATIONS OF INTEGRALS

    PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

Similar Questions

Explore conceptually related problems

y = 5 cos x - 3 sin x , prove that (d^2 y)/(dx^2) + y = 0

If y = 2 cos x -6 sin x , prove that (d^2y)/(dx^2)+y = 0

If y = e^x (sinx + cosx) , prove that (d^2y)/(dx^2)- 2(dy)/(dx) + 2y = 0

If x = a cos θ + b sin θ and y = a sin θ − b cos θ , then prove that y^2(d^2y)/(dx^2)-x(dy)/(dx) +y=0

If y = tan x + sec x , prove that (d^2y)/(dx^2) = (cosx)/((1-sinx)^2)

Find the second order derivative of the following functions If y = x + tan x , prove that cos^2 x . (d^2 y)/(dx^2) - 2y + 2x = 0

PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find the second order derivative of the following functions If y = a...

    Text Solution

    |

  2. If x cos (a+y) = cos y, then prove that dy/dx = (cos^2(a+y))/(sina) He...

    Text Solution

    |

  3. If y = 2 sin x + 3 cos x, prove that y + (d^2y)/(dx^2) = 0

    Text Solution

    |

  4. If y = a cos m x + b sin m x , prove that y 2 +m^2 y = 0

    Text Solution

    |

  5. Find the second order derivative of the following functions If y = l...

    Text Solution

    |

  6. If y= [Log(x+sqrt(x^2+1))]^2 then show that (x^2+1)y2+xy1=0

    Text Solution

    |

  7. Find the second order derivative of the following functions If y = (...

    Text Solution

    |

  8. If x = tan(1/a logy), then show that (1+X^2) (d^2y)/(dx^2) + (2x -a) d...

    Text Solution

    |

  9. If y = x^x, prove that y2 - y^-1 (y1)^2 - yx^-1 = 0

    Text Solution

    |

  10. If y = (tan^-1 x)^2, then prove that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^...

    Text Solution

    |

  11. If y=[sin^-1 x]^2, then prove that : (1 -x^2) y2-xy1 - 2 = 0.

    Text Solution

    |

  12. Find the second order derivative of the following functions If y = c...

    Text Solution

    |

  13. If y = cosec^-1x,x>1, then show that : x(x^2-1)(d^2y)/(dx^2) + (2x^2-1...

    Text Solution

    |

  14. If y = x^x, prove that y2 - y^-1 (y1)^2 - yx^-1 = 0

    Text Solution

    |

  15. If y = e^(-ax) cos (bx + c), show that (d^2y)/(dx^2) + 2a(dy)/(dx) + ...

    Text Solution

    |

  16. If y^2 = ax^2 + b, prove that (d^2y)/(dx^2) = ab/y^3

    Text Solution

    |

  17. If x^2 + y^2 = a^2, prove that (d^2y)/(dx^2) = -a^2/y^3

    Text Solution

    |

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

    Text Solution

    |

  19. If x^2/a^2 + y^2/b^2 = 1, prove that (d^2y)/(dx^2) = -(b^4)/(a^2y^3)~

    Text Solution

    |

  20. If sqrtx + sqrty = sqrtx , find (d^2y)/(dx^2) at x = a

    Text Solution

    |