Home
Class 12
MATHS
If y=x^n{acos(logx)+bsin(logx)} , prove ...

If `y=x^n{acos(logx)+bsin(logx)}` , prove that `x^2\ (d^2y)/(dx^2)+(1-2n)(dy)/(dx)+(1+n^2)y=0` .

Text Solution

AI Generated Solution

To prove that \[ x^2 \frac{d^2y}{dx^2} + (1 - 2n) \frac{dy}{dx} + (1 + n^2)y = 0 \] for ...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If y=Acos(logx)+B sin(logx) then prove that x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0 .

If y=asin(logx)+bcos(logx) , prove that : x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0 .

If y=a cos (logx)+b sin (logx) , prove that x^(2)y_(2)+xy_(1)+y=0 .

If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2=0 .

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

If y=sin^(-1)x, prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=0

If y=sin^(-1)x ,then prove that (1-x^(2))(d^(2)y)/(dx^(2))=x(dy/dx)

If y=tan^(-1)x, prove that (1+x^(2))(d^(2)y)/(dx^(2))(2x)(dy)/(dx)=0

If y=acos(lnx)+bsin(lnx) then prove that x^2y_3+3x y_2+2y_1=0

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. Find A\ a n d\ B so that y=Asin3x+Bcos3x satisfies the equation (d^2y)...

    Text Solution

    |

  2. If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...

    Text Solution

    |

  3. If y=x^n{acos(logx)+bsin(logx)} , prove that x^2\ (d^2y)/(dx^2)+(1-2n)...

    Text Solution

    |

  4. If y=a[x+(x^2-1)^(1/2)]^n+b[x-(x^2-1)^(1/2)]^n the value of the expre...

    Text Solution

    |

  5. If y=a\ x^(n+1)+b x^(-n) and x^2(d^2y)/(dx^2)=lambday , then write the...

    Text Solution

    |

  6. If x=acosn t-bsinn t and (d^2x)/(dt^2)=lambdax , then find the value ...

    Text Solution

    |

  7. If x=t^2 and y=t^3 , find (d^2y)/(dx^2) .

    Text Solution

    |

  8. If x=2a t , y=a t^2 , where a is a constant, then find (d^2y)/(dx^2...

    Text Solution

    |

  9. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

    Text Solution

    |

  10. If y=1-x+(x^2)/(2!)-(x^3)/(3!)+(x^4)/(4!)...... oo , then write (d^2y)...

    Text Solution

    |

  11. If y=x+e^x , find (d^2x)/(dy^2) .

    Text Solution

    |

  12. If y=|x-x^2| , then find (d^2y)/(dx^2) .

    Text Solution

    |

  13. If y=|(log)e x| , find (d^2y)/(dx^2) .

    Text Solution

    |

  14. If x=acosnt-bsinnt , then (d^2x)/(dt^2) is (a)n^2x (b) -n^2x (c) n x ...

    Text Solution

    |

  15. If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= -1/(t^2) (b) 1/(2\ a t^...

    Text Solution

    |

  16. If y=a x^(n+1)+b x^(-n) , then x^2(d^2y)/(dx^2)= (a)n(n-1)y (b) n(n+1...

    Text Solution

    |

  17. (d^(20))/(dx^(20))(2cosxcos3x)= 2^(20)(cos2x-2^(20)cos4x) (b) 2^(20)(...

    Text Solution

    |

  18. If x=t^2,\ \ y=t^3 , then (d^2y)/(dx^2)= (a)3//2 (b) 3//4t (c) 3//2t ...

    Text Solution

    |

  19. If y=a+b x^2,\ a ,\ b arbitrary constants, then (d^2y)/(dx^2)=2\ x y...

    Text Solution

    |

  20. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)ddot(cosn x+isinn x) a...

    Text Solution

    |