Home
Class 12
MATHS
If y = ae^(x) + be^(-x) + c, where a, b,...

If `y = ae^(x) + be^(-x) + c`, where a, b, c are parameters, then y'' is equal to

A

0

B

y'

C

y

D

y''

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    SIA PUBLICATION|Exercise Problems|48 Videos
  • EAMCET - 2018 (TS) SHIFT - 1

    SIA PUBLICATION|Exercise EXERCISE - Chemistry|8 Videos

Similar Questions

Explore conceptually related problems

y = ae^(3x) + be^(-2x)

The differential equation whose solution is y = Ae^(3x) + Be^(-3x) , where A, B are arbitrary constant, is

The differential equation of the family y = ae^(x) + bx e^(x) + cx^(2) e^(x) of curves, where a, b, x are arbitrary constant is

Form the differential equations corresponding to the family of curves. (i) y = c(x-2c) where c is a parameter. (ii) y = a cos 3x + b sin 3x where a, b are parameters. (iii) y = a cos x + b sin x where a, b are parameters. (iv) y = a e^(x) + b e^(-x) where a, b are parameters.

Find the order of the differential equation corresponding to (i) y = c(x-c)^(2) where c is an arbitrary constant. (ii) y = Ae^(x) + Be^(3x) + Ce^(5x) where A, B, C are arbitrary constant. (iii) xy = c e^(x) + b e^(-x) + x^(2) where b, c are arbitrary constants. (iv) The family of all circles in the xy-plane with centre at the origin.

The condition for the coaxial system x^(2) + y^(2) + 2 lambda x + c = 0 , where lambda is parameter and c is a constant , to have distinct limiting points is

The differential equation representing the family of curves y^(2) = 2c (x + sqrtc) , where c gt 0 is a parameter, is of order and degree as follows.

The differential equation corresponding to the family of circles given by (x-a)^(2) + (y-b)^(2) = 4 where a and b are parameters, is

SIA PUBLICATION-DIFFERENTIATION -Problems
  1. If 2x^(2) - 3xy + y^(2) + x + 2y - 8 = 0, then (dy)/(dx) is equal to

    Text Solution

    |

  2. If y = log {((1 +x)/(1-x )) ^(1//4) } -1/2 Tan ^(-1) (x ), then (dy)/(...

    Text Solution

    |

  3. x = cos theta, y = sin 5 theta implies (1- x ^(2)) (d^(2)y)/(dx ^(2)) ...

    Text Solution

    |

  4. x ^(y) =y ^(x) implies x ( x-y log x ) (dy)/(dx) =

    Text Solution

    |

  5. If f(x) = e^(x) sin x, then f^((6)) (x) is equal to

    Text Solution

    |

  6. IF f : R to R is an even function which is twice differentiable on R a...

    Text Solution

    |

  7. Statement I : f(x) = ax^(41) + bx^(-40) rArr (f'(x))/(f(x)) = 1640...

    Text Solution

    |

  8. f (x) = 10 cos x + (13 + 2x) sin x implies f''(x) + f(x) =

    Text Solution

    |

  9. x sqrt(1 + y) + y sqrt(1 + x) =0implies (dy)/(dx)=

    Text Solution

    |

  10. If x ^(y) = e ^(x -y) then (dy)/(dx) =

    Text Solution

    |

  11. y = Sin ^(-1) x implies ( 1- x ^(2)) (d ^(2) y)/(dx ^(2)) =

    Text Solution

    |

  12. If f(x) = (1)/(x^(2)) int(3)^(x)(2t-3f'(t)dt, then f'(3) is equal to

    Text Solution

    |

  13. If f (x) = e ^(x) , g (x) = Sin ^(-1) x and h (x) =f (g (x)), then (h'...

    Text Solution

    |

  14. If y = sqrt(ax) + (a ^(2))/(sqrt(ax))then y (1) , y (2) at x =a are

    Text Solution

    |

  15. If y = ae^(x) + be^(-x) + c, where a, b, c are parameters, then y'' is...

    Text Solution

    |

  16. If y =a cos (log x) + b sin (log x) then x ^(2) y (2) + xy (1)+y=

    Text Solution

    |

  17. If h (x) = e ^(e ^(x)) then (h '(x))/( h(x))

    Text Solution

    |

  18. (d)/(dx) {Sin ^(-1) (3x -4 x ^(3))}=

    Text Solution

    |

  19. If y (k) is the kth derivative of y with respect to x,y= cos (sin x) ...

    Text Solution

    |

  20. If f(x) = (x^(2))/(x+a), then f''(a) is equal to

    Text Solution

    |