Home
Class 12
MATHS
If y = (x+ sqrt(1+x^2))^n then prove tha...

If `y = (x+ sqrt(1+x^2))^n` then prove that `(1+x^2)y_2+xy_1 = n^2y`.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

IF y=(x+sqrt(1+x^2))^n , Prove that, (1+x^2)y_2+xy_1=n^2y . Hence, find the value of (y_2)_0 .

If (sqrt(1-x^2))y= sin^(-1)x then show that (1-x^2)y_2-3xy_1-y =0

if y = (x+sqrt(x^2+a^2))^n then prove that (dy)/(dx)= (ny)/(sqrt(x^2+a^2)

If y="("x+sqrt(x^(2)-1)")"^(m) , then prove that, (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+m^(2)y=0

If y=log(x+sqrt(x^2+a^2)) , show that (a^2+x^2)y_2+xy_1=0

IF y=cos (m sin^-1 x), prove that , (1-x^2)y_2-xy_1+m^2y=0 .

IF y=x^2 cosx, prove that , x^2y_2-4xy_1+(x^2+6)y=0 .

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

If 2x= y^(1/5)+y^(-1/5) prove that (x^2-1)y_2+xy_1 = 25y

If y=sin(logx), prove that , x^2y_2+xy_1+y=0 .

UNITED BOOK HOUSE-SET 6-EXERCISE
  1. Solve: (1+x^2)(dy)/(dx) = y+tan^(-1)x

    Text Solution

    |

  2. If vec p is a unit vector and (vec x- vecp).(vec x+ vecp) = 8 then fin...

    Text Solution

    |

  3. Find the intercepts made by the plane x-2y+3z-18=0 on the axes.

    Text Solution

    |

  4. If P(A) = 5/13,P(B)= 6/13 and P(AuuB) = 7//13 then find P(bar A//B) a...

    Text Solution

    |

  5. The mean and variance of a binomial distribution are 16 and 12 respect...

    Text Solution

    |

  6. Prove that tan^(-1) {(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cos x)-sqrt(...

    Text Solution

    |

  7. Let A = [[1,0],[-1,7]] and I = [[1,0],[0,1]] then find the K when A^2=...

    Text Solution

    |

  8. Show that A = [[1,2,2],[2,1,2],[2,2,1]] satrisfies the matrix equation...

    Text Solution

    |

  9. If alpha,beta,gamma are in A.P. then show that , |[x-3,x-4,x-alpha],[x...

    Text Solution

    |

  10. If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2...

    Text Solution

    |

  11. If y = (x+ sqrt(1+x^2))^n then prove that (1+x^2)y2+xy1 = n^2y.

    Text Solution

    |

  12. Evaluate: int (dx)/(1+tanx)

    Text Solution

    |

  13. Evaluate: int e^x (2-sin 2x)/(1-cos 2x)dx

    Text Solution

    |

  14. Solve: (x+3)(dy)/(dx)-3y =(x+3)^5

    Text Solution

    |

  15. Solve: y^2dx+(xy+x^2)dy =0

    Text Solution

    |

  16. If vec axx vec b= vec cxxvec d and vec axxvec c= vec bxxvec d, vec a n...

    Text Solution

    |

  17. A and B toss a coin alternately untill one of them gets a head for the...

    Text Solution

    |

  18. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

    Text Solution

    |

  19. Prove that the perpendicular distance of the line 3x+4y+5 =0 from ori...

    Text Solution

    |

  20. If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx ...

    Text Solution

    |