Home
Class 12
MATHS
The function u=e^x s in ; v=e^x cos x sa...

The function `u=e^x s in ; v=e^x cos x` satisfy the equation `v(d u)/(dx)-u(d v)/(dx)=u^2+v^2` b. `(d^2u)/(dx^2)=2v` c. `(d^2)/(dx^2)=-2u` d. `(d u)/(dx)+(d v)/(dx)=2v`

A

`v(du)/(dx)-u(dv)/(dx)=u^(2)+v^(2)`

B

`v(d^(2)u)/(dx^(2))=2v`

C

`(d^(2)v)/(dx^(2))=-2u`

D

All of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

The function u=e^(x)sin x,v=e^(x)cos x satisfy the equation (a) v(du)/(dx)-u(du)/(dx)=u^(2)+v^(2)(b)(d^(2)u)/(dx^(2))=2v(c)d^(2)v())/(dx^(2))=-2u(d)(du)/(dx)+(dv)/(dx)=2v

int(u(v(du)/(dx)-u(dv)/(dx)))/(v^(3))dx=

If u=e^(ax)sinbx and v=e^(ax)cosbx . then what is u(du)/(dx)+v(dv)/(dx) equal to ?

If : (dx)/(dy)=u" and "(d^(2)x)/(dy^(2))=v," then: "(d^(2)y)/(dx^(2))=

u=(x^(2)-y^(2))/(x^(2)+y^(2)) find d(u)/(dx)?

D(u+-v)=D(u)+-D(v)

If e^(v)+e^(u)=e^(v+u) , then (du)/(dv)=

If u and v are two functions of x then prove that: int uvdx=u int vdx-int[(du)/(dx)int vdx]dx

Let u(x) and v(x) satisfy the differential equation (du)/(dx)+p(x)u=f(x) and (dv)/(dx)+p(x)v=g(x) are continuous functions.If u(x_(1)) for some x_(1) and f(x)>g(x) for all x>x_(1), does not satisfy point (x,y), where x>x_(1), does not satisfy the equations y=u(x) and y=v(x) .

If u=inte^(ax)sin " bx dx" and v=inte^(ax)cos " bx dx then "(u^(2)+v^(2))(a^(2)+b^(2))=

ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. Let f(x)=x^(n) , n being a non-negative integer, The value of n for w...

    Text Solution

    |

  2. If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the grea...

    Text Solution

    |

  3. The function u=e^x s in ; v=e^x cos x satisfy the equation v(d u)/(dx)...

    Text Solution

    |

  4. If f(x)=logx(lnx) then f'(x) at x=e is

    Text Solution

    |

  5. Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for ...

    Text Solution

    |

  6. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

    Text Solution

    |

  7. If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo)))), then (dy)/(dx) is equal to

    Text Solution

    |

  8. If f(x)=|cosx-sinx| , then f'(pi/4) is equal to

    Text Solution

    |

  9. Let f(x)=x^2+xg^2(1)+g^''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then fin...

    Text Solution

    |

  10. if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) +...

    Text Solution

    |

  11. If y+log(1+x)=0 which of the following is true?

    Text Solution

    |

  12. If y=2^(3^(x)), then y' equals

    Text Solution

    |

  13. If g is the inverse of fandf(x) = x^(2)+3x-3,(xgt0). then g'(1) equal...

    Text Solution

    |

  14. If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n y^(prime)(1)=4/3 (b) y^(1)...

    Text Solution

    |

  15. let y=sqrt(x+sqrt(x+sqrtx...oo))) then dy//dx equals

    Text Solution

    |

  16. Ify=x^((lnx)^ln(lnx)) , then (dy)/(dx) is equal to

    Text Solution

    |

  17. Which of the following functions are not derivable at x=0?

    Text Solution

    |

  18. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1).x then

    Text Solution

    |

  19. If 2^(x)+2^(y)=2^(x+y) then (dy)/(dx)is equal to

    Text Solution

    |

  20. For the function y=f(x)=(x^(2)+bx+c)e^(x), which of the following hold...

    Text Solution

    |