Home
Class 12
MATHS
If y=xln((a x)^(-1)+a^(-1)) prove that x...

If `y=xln((a x)^(-1)+a^(-1))` prove that `x(x+1)(d^2y)/(dx^2)+(dy)/(dx)=y=1`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Ify=x log[(ax)^(-1)+a^(-1)], prove that x(x+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)=y-1

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

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

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

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

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

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

If y=sqrt(x+1)-sqrt(x-1) ,prove that (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx)-(y)/(4)=0

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

RESONANCE DPP-JEE MAINS-All Questions
  1. If (lim)(xvecoo)(2+(f(x))/(x^2))^(1/x)=e and f(x)=a0+a1x+a2x^3+ , then

    Text Solution

    |

  2. The matrix A has x rows and (x+5) column. If the matrix B has y rows a...

    Text Solution

    |

  3. If y=xln((a x)^(-1)+a^(-1)) prove that x(x+1)(d^2y)/(dx^2)+(dy)/(dx)=y...

    Text Solution

    |

  4. If the solution of the equation |(x^4-9)-(x^2+3)|=|x^4-9|-|x^2+3| is ...

    Text Solution

    |

  5. In the given figure (circle), P T=5,P D=7a n dP A=2, then the value of...

    Text Solution

    |

  6. Consider the matrices A=[4 6-1 3 0 2 1-2 5],B=[2 4 0 1-1 2],C=[3 1 2]...

    Text Solution

    |

  7. The solution set of the equation, (x+1)log3 2x+4x(log)3x-16=0 is an ...

    Text Solution

    |

  8. If y = f(x),has following graph Match the column by filling follo...

    Text Solution

    |

  9. Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not e...

    Text Solution

    |

  10. If {.} represents fractional part function and {x}+{-x}=x^2+x-6 , then...

    Text Solution

    |

  11. Line x/a+y/b=1 cuts the co-ordinate axes at A(a,0) and B(0,b) and the ...

    Text Solution

    |

  12. Let (81^(1/((log)5 9))+3^(3/(log(sqrt(6))3)))/(409)dot((sqrt(7))2/((l...

    Text Solution

    |

  13. A curve with equation of the form y=a x^4+b x^3+c x+d has zero gradien...

    Text Solution

    |

  14. Complete solution of inequality ||3x-9|+2|>2 is (-oo,oo) (b) {3} (...

    Text Solution

    |

  15. vec axx( vec bxx vec c) , vec bxx( vec cxx vec a) and vec cxx( vec a...

    Text Solution

    |

  16. If 1/3(log)3M+3(log)3N=1+(log)(0. 008)5, then M^9=9/N (b) N^9=9/M M^...

    Text Solution

    |

  17. Let f: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then ...

    Text Solution

    |

  18. e^(2x)-(a-1)e^x-ageq0AAx in R , then values of a which satisfy are. (...

    Text Solution

    |

  19. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

    Text Solution

    |

  20. The solution set of the equation 4s inthetadotcostheta-2costheta-2sqrt...

    Text Solution

    |