Home
Class 12
MATHS
Let y = (sin^(-1)x)^2+(cos^(-1)x)^2 show...

Let `y = (sin^(-1)x)^2+(cos^(-1)x)^2` show that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=4`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let y=(sin^-1x)^2+(cos^-1x)^2 , show that, (1-x^2)(d^2y)/(dx^2)-xdy/dx=4

If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

If y=(sin^(-1)x)^(2)+(cos^(-1)x)^(2) , then show that, (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=4

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

If y=(sin^(-1) x)/(sqrt(1-x^2)) , then show that (1-x^2)(d^2y)/(dx^2)-3x(dy)/(dx)-y=0 .

If y=cos(2sin^(-1)x) , then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+4y=0

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

If y= e^(a cos^(-1)x), -1 le x le 1 , show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0 .

answer the foll. Questions: (i) if y=(sin^(-1)x)/(sqrt(1-x^2)) , then show that (1-x^2) (d^2y)/dx^2-3x dy/dx -y=0

If y=e^(acos^(-1)x),-1lt=x<1,s how t h a t (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0

UNITED BOOK HOUSE-SET 9-EXERCISE
  1. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

    Text Solution

    |

  2. If A = [[3,1],[-1,2]],I= [[1,0],[0,1]] and O = [[0,0],[0,0]] show that...

    Text Solution

    |

  3. Show that, A = 1/3[[1,2,2],[2,1,-1],[-2,2,-1]] are orthogonal matrix a...

    Text Solution

    |

  4. Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

    Text Solution

    |

  5. Show that the following determinant is a perfect square |[1,a,a^2],[a^...

    Text Solution

    |

  6. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

    Text Solution

    |

  7. Let y = (sin^(-1)x)^2+(cos^(-1)x)^2 show that (1-x^2)(d^2y)/(dx^2)-x(d...

    Text Solution

    |

  8. Evaluate: int (dx)/(1+x^3)

    Text Solution

    |

  9. Evaluate: int (x^2dx)/(x^4-x^2+1).

    Text Solution

    |

  10. Solve: xdx+ ydy+ (xdy-ydx)/(x^2+y^2)=0 given y = 1 when x= 1.

    Text Solution

    |

  11. Solve: (x+tany)dy = sin 2y dx.

    Text Solution

    |

  12. D,E,F are the midpoints of the sides bar(BC),bar(CA) and bar(AB) respe...

    Text Solution

    |

  13. The dot product of a vector with the vectors hat i-3 hatk,hat i-2 hatk...

    Text Solution

    |

  14. Evalute: overset(pi//2)underset(0)int sin^(3//2)x/(sin^(3//2)x+cos^(3/...

    Text Solution

    |

  15. The probability distribution of a discrete random varible X is as fol...

    Text Solution

    |

  16. A ballong leaves the ground 50 ft from an observer. If it rises vertic...

    Text Solution

    |

  17. A particle moves in a straight line such that its distance x from a fi...

    Text Solution

    |

  18. Find the area of the region {(x , y): y^2lt=4x ,4x^2+4y^2lt=9}

    Text Solution

    |

  19. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/4...

    Text Solution

    |

  20. Find the distance between the point P(6,5,9) and the plane passing thr...

    Text Solution

    |