Home
Class 12
MATHS
If y=e^tan^((-1)x) , prove that (1+x^2)y...

If `y=e^tan^((-1)x)` , prove that `(1+x^2)y_2+(2x-1)y_1=0` .

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If log y=tan^(-1)x, show that (1+x^(2))y_(2)+(2x-1)y_(1)=0

If y=e^acos^((-1)x) , then prove that (1-x^2)y_2-x y_1-a^2y=0 .

If y=(sin^(-1)x)^(2), prove that (1-x^(2))y_(2)-xy_(1)-2=0

If y=e^(m sin^(-1)x) then prove that (1-x^2) y_2 - xy_1 = m^2 y

If y=(tan^(-1)x)^2 , show that (x^2+1)^2y_2+2x(x^2+1)y_1=2 .

If quad y=(sin^(-1)x)^(2), prove that (1-x^(2))y_(2)-xy_(1)-2=0

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

If y=e^(mtan^(-1)x) , prove that : (1+x^(2))(d^(2)y)/(dx^(2))+(2x-m)dy/dx=0 .

If y=sin(mtan^(-1)x) , prove that : (1+x^(2))^(2)y_(2)+2x(1+x^(2))y_(1)+m^(2)y=0 .

If y=(tan^(-1)x)^(2), then prove that (1+x^(2))^(2)y_(2)+2x(1+x^(2))y_(1)=2

BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If (x-a)^2+(y-b)^2=c^2\ \ (c >0) then ([1+((dy)/(dx))^2]^(3//2))/((d^2...

    Text Solution

    |

  2. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

    Text Solution

    |

  3. If y=e^tan^((-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .

    Text Solution

    |

  4. If y=e^(asin^(-1)x) then show that (1-x^2)y(n+2)-(2n+1)xy(n+1)-(n^2+a^...

    Text Solution

    |

  5. Find (dy)/(dx), if x=acostheta , y=asintheta

    Text Solution

    |

  6. Find (dy)/(dx) , if x=a t^2 , y=2a t

    Text Solution

    |

  7. Find (dy)/(dx) , if x^(2/3) +y^(2/3)=a^(2/3)

    Text Solution

    |

  8. Find (dy)/(dx) , if x=2a t^2 , y=a t^4

    Text Solution

    |

  9. Find (dy)/(dx) , if x=(sin^3t)/(sqrt(cos2t)) , y=(cos^3t)/(sqrt(cos2t)...

    Text Solution

    |

  10. Find (dy)/(dx) , if x=acostheta , y=bcostheta

    Text Solution

    |

  11. Find (dy)/(dx) , if x=costheta-cos2theta , y=sintheta-sin2theta

    Text Solution

    |

  12. Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...

    Text Solution

    |

  13. Find (dy)/(dx) , if x=a(cost+logtant/2) , y=asint

    Text Solution

    |

  14. Find (dy)/(dx) , if x=asectheta , y=btantheta

    Text Solution

    |

  15. Find (dy)/(dx) , if x=a(costheta+thetasintheta) , y=a(sintheta-thetaco...

    Text Solution

    |

  16. If x=sqrt(a^sin^((-1)t)) , y=sqrt(a^cos^((-1)t)) , show that (dy)/(...

    Text Solution

    |

  17. If y = x^3 + tan x, show that (d^2y)/dx^2= 6x + 2 sec^2 tanx.

    Text Solution

    |

  18. If y=3e^(2x)+2e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

    Text Solution

    |

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

    Text Solution

    |

  20. If y=5cosx-3sinx , prove that (d^2y)/(dx^2)+y=0 .

    Text Solution

    |