Home
Class 12
MATHS
If y=3 cos (log x)+4 sin (log x) Show th...

If `y=3 cos (log x)+4 sin (log x)` Show that `x^2 y_2+x y_1+y=0`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    V PUBLICATION|Exercise QUESTION BANK|45 Videos

  • DETERMINANT

    V PUBLICATION|Exercise QUESTION BANK|136 Videos

Similar Questions

Explore conceptually related problems

If y=a cos(log x)+b sin(logx) , Prove that x^2y_2+xy_1+y=0 .

Let y=3cos(logx)+4sin(logx) Prove that x^2y_2+xy_1+y=0

a) Find (dy/dx) if i) y=sin (x^3+7) ii) x=a(t-sin t), y=a(1-cos t) b) If y=a cos (log x)+b sin (log x) Prove that x^2 (d^2 y)/(d x^2)+x (dy/dx)+y=0

If x=sint and y=sinmt show that (1-x^2)y_2-xy_1+m^2y=0

If y=e^(acos^-1x) , then show that (1-x^2)y_2-xy_1-a^2y=0

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

If y = log ( 1 + sin x) , prove that y_(4) + y_(3) y_(1) + y_(2)^(2) = 0

If y=(tan^(-1)x)^2 , show that (x^2+1)^2y_2+2x(x^2+1)y_1=2 .

Given that logy=tan^-1x . Show that (1+x^2)y_2+(2x-1)y_1=0

If y=log(1/x) , show that dy/dx+e^y=0

V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If y=5 cos x-3 sin x, prove that (d^2y)/(dx^2)+y=0

    Text Solution

    |

  2. If y=cos ^(-1) x find (d^2y)/(dx^2) in terms of y alone.

    Text Solution

    |

  3. If y=3 cos (log x)+4 sin (log x) Show that x^2 y2+x y1+y=0

    Text Solution

    |

  4. If y=ae^(mx)+be^(nx) , show that (d^2y)/(dx^2)-(m+n)dy/dx+mny=0

    Text Solution

    |

  5. If y=500e^(7x)+600e^(-7x). Show that (d^2y)/(dx^2)=49y

    Text Solution

    |

  6. If e^y(x+1)=1 , show that (d^2y)/(dx^2)=(dy/dx)^2

    Text Solution

    |

  7. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

    Text Solution

    |

  8. Verify Rolle's theorem for the function f(x)=x^2+2 in the interval [...

    Text Solution

    |

  9. Verify Mean Value Theorem for the function f(x)=x^2 in the interval [2...

    Text Solution

    |

  10. Verify Rolle's Theorem for the function f(x)=x^2+2x-8 , x in [-4,2]

    Text Solution

    |

  11. If f:[-5,5]toR is a differentiable function and if f'(x) does not vani...

    Text Solution

    |

  12. Verify mean value theorem for the function f(x)=x^2-4x-3 in the interv...

    Text Solution

    |

  13. Verify Lagrange 's mean value theorem, if f(x)=x^3-5x^2-3x in the inte...

    Text Solution

    |

  14. Differentiate w.r.t. x, the following functions: (i) sqrt(3 x+2)+1/(s...

    Text Solution

    |

  15. Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^...

    Text Solution

    |

  16. Find f'(x) if f(x)=(sin x)^(sin x) for all 0ltxltpi

    Text Solution

    |

  17. For a positive constant a find (dy/dx), where y=a^(t+1/t), and x=(t+1/...

    Text Solution

    |

  18. Differentiate sin ^2 x w.r.t e^(cos x)

    Text Solution

    |

  19. Differentiate w.r.t x the function (3 x^2-9 x+5)^9

    Text Solution

    |

  20. Differentiate w.r.t x the function sin ^3 x+cos ^6 x

    Text Solution

    |