Home
Class 12
MATHS
If y=500e^(7x)+600e^(-7x). Show that (d^...

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

Text Solution

Verified by Experts

`y=500e^(7x)+600e^(-7x)dy/dx=7(500e^(7x))-7(600e^(-7x)),(d^2y)/dx=49(500e^(7x)+49(600e^(-7x)=49y`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|47 Videos

  • DETERMINANTS

    A N EXCEL PUBLICATION|Exercise QUESTION TYPE|83 Videos

Similar Questions

Explore conceptually related problems

If y=ae^(5x)+be^(-5x) , show that (d^2y)/(dx^2)-25y=0

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

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

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

If e^y(x+1)=1 . Show that dy/dx=-e^y

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

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

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

If y=sin^-1x ,then show that (1-x^2)(d^2y)/dx^2-xdy/dx=0

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

A N EXCEL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let y=3cos(logx)+4sin(logx) Prove that x^2y2+xy1+y=0

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Examine if Rolle's theorem is applicable to any of the following funct...

    Text Solution

    |

  8. Examine if Rolle's theorem is applicable to any of the following funct...

    Text Solution

    |

  9. Examine if Rolle's theorem is applicable to any of the following funct...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Differentiate the following w.r.t x sin^3x+cos^6x

    Text Solution

    |

  15. Differentiate the following w.r.t x (5x)^(3cos2x)

    Text Solution

    |

  16. Differentiate the following w.r.t x (logx)^(logx),xgt1

    Text Solution

    |

  17. Differentiate the following w.r.t.x x^x+x^a+a^x+a^a for some fixed agt...

    Text Solution

    |

  18. Find dy/dx,if y=12(1-cost),x=10(t-sint).pi/2lttltpi/2

    Text Solution

    |

  19. If x= a(cos t +t sin t) and y=a(sin t - t cos t), find (d^2y)/(dx^2)

    Text Solution

    |

  20. If y=e^(acos^-1x) , then show that (1-x^2)y2-xy1-a^2y=0

    Text Solution

    |