Home
Class 12
MATHS
If y=e^x(sinx+cosx) prove that (d^2y)/(d...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|406 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

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

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

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

If y= cot x, prove that (d^(2)y)/(dx^(2)) + 2y (dy)/(dx)= 0.

If y=e^(ax) sin bx then prove that (d^2y)/(dx^(2))-2a(dy)/(dx)+(a^(2)+b^(2))y=0 .

If y=3\ e^(2x)+2\ e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

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

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

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

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. Find (d^2y)/(dx^2) , where y=log((x^2)/(e^2)) .

    Text Solution

    |

  2. If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If y=e^(acos^(-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x...

    Text Solution

    |

  6. If y=500\ e^(7x)+600\ e^(-7x) , show that (d^2y)/(dx^2)=49\ y .

    Text Solution

    |

  7. If x=2cost-cos2t ,\ \ y=2sint-sin2t , find (d^2y)/(dx^2) at t=pi/2 .

    Text Solution

    |

  8. If x=4z^2+5,\ \ y=6z^2+7z+3, find (d^2y)/(dx^2) .

    Text Solution

    |

  9. If y=log(1+cosx) , prove that (d^3y)/(dx^3)+(d^2y)/(dx^2)dot(dy)/(dx)=...

    Text Solution

    |

  10. If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

    Text Solution

    |

  11. If y=3\ e^(2x)+2\ e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

    Text Solution

    |

  12. If y=(cot^(-1)x)^2 , prove that y2(x^2+1)^2+2x(x^2+1)y1=2 .

    Text Solution

    |

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

    Text Solution

    |

  14. If x=cost+logtan(t/2),\ \ y=sint , then find the value of (d^2y)/(dt^2...

    Text Solution

    |

  15. If x=asint and y=a(cost+logtan(t/2)) , find (d^2y)/(dx^2) .

    Text Solution

    |

  16. If x=a(cost+tsint) and y=a(sint-tcost) , then find the value of (dy)...

    Text Solution

    |

  17. If x=a(cost+logtan(t/2)) , y=asint , evaluate (dy)/(dx) .

    Text Solution

    |

  18. If x=a(cos2t+2tsin2t) and y=a(sin2t-2tcos2t) , then find (dy)/(dx) .

    Text Solution

    |

  19. If x=asint-bcost ,\ \ y=acost+bsint ,find (dy)/(dx) .

    Text Solution

    |

  20. Find A\ a n d\ B so that y=Asin3x+Bcos3x satisfies the equation (d^2y)...

    Text Solution

    |