Home
Class 12
MATHS
If y= [Log(x+sqrt(x^2+1))]^2 then show t...

If `y= [Log(x+sqrt(x^2+1))]^2` then show that `(x^2+1)y_2+xy_1=0`

Promotional Banner

Topper's Solved these Questions

  • RELATION & FUNCTIONS

    JMD PUBLICATION|Exercise EXERCISE|21 Videos

  • VECTOR ALGEBRA

    JMD PUBLICATION|Exercise EXAMPLE|54 Videos

Similar Questions

Explore conceptually related problems

If sqrt(x^2 +1) y = log(sqrt(x^2+1)-x) , then show that (x^2 +1) dy/dx + xy + 1=0

If y = (sqrt(x+1) - sqrt(x-1)) , then prove that (x^2-1) y_2 +xy_1 = 1/4 y

y = [x + sqrt(x^2 + 1)]^p , prove that (x^2 + 1)y_2 + xy_1 - p^2y = 0

If y = [ x + 5 + sqrt(x^2 + 10x + 1)]^n then prove that (x^2 + 10x + 1) y_2 + (x + 5) y_1 - n^2y = 0 .

IF y =[log (x+ sqrt(1+ x^2))]^2 ,show that (1+ x^2) (d^2y) /dx^2 +x(dy/dx) =0

If y = log (x + sqrt(x^2+1))/(sqrt(x^2+1)) , prove that (x^2 +1) dy/dx + xy = 1

Find the second order derivative of the following functions If y = log[x + sqrt(x^2 + a^2)] , show that (x^2 + a^2) (d^2y)/(dx^2) + x (dy)/(dx) = 0

If ysqrt(x^(2)+1)=log(x+sqrt(x^(2)+1)) , show that (x^(2)+1)(dy)/(dx)+xy-1=0 .

JMD PUBLICATION-SOLVED SAMPLE QUESTION PAPERS-EXAMPLE
  1. Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^...

    Text Solution

    |

  2. If x^y+y^x= (x+y)^(x+y), then prove that dy/dx= ((x+y)^(x+y) [1+log(x+...

    Text Solution

    |

  3. If y= [Log(x+sqrt(x^2+1))]^2 then show that (x^2+1)y2+xy1=0

    Text Solution

    |

  4. Evaluate intdx/(sinx-sin2x)

    Text Solution

    |

  5. Solve (3xy+y^2)dx+(x^2+xy)dy=0, y(1)=1

    Text Solution

    |

  6. solve the differential equation: dy/dx=tan(x+y)

    Text Solution

    |

  7. A car manufacturing factory has to plant s X and Y. Plan X manufacture...

    Text Solution

    |

  8. Solve the following system of linear equations by matrix method: x - y...

    Text Solution

    |

  9. If A= [[1,2,2,],[2,1,2,],[2,2,1,]] then verify A^-1A=I

    Text Solution

    |

  10. Find the shortest distance (S.D.) between the lines : vec r = hat i + ...

    Text Solution

    |

  11. Find the equation of the perpendicular drawn from the point (2,4,-1) t...

    Text Solution

    |

  12. Maximise z=20x+15y subject to constraints 120x +60yle12000,x+yle150

    Text Solution

    |

  13. Maximise z=x+y subject to 2x+yle50, x+2y=40

    Text Solution

    |

  14. The number of bijective functions from A to B if n(A)=n(B)=4

    Text Solution

    |

  15. The value of sin(cos^-1(3/5)) is:

    Text Solution

    |

  16. If AB=A and BA=B, then B^2=

    Text Solution

    |

  17. If A is a square matrix of order 3 such that |A|=13, then |adj A| is e...

    Text Solution

    |

  18. If f(x)= {(1,-,kx, x,le3),(2x,+,3,x,>3):} is a continuous function, t...

    Text Solution

    |

  19. If f(x) = {((tan3x)/(x),,, x!=0,),(4k,,,x,=0):} is continuous at x=0' ...

    Text Solution

    |

  20. d/dx{tan^-1sqrtx}=

    Text Solution

    |