Home
Class 12
MATHS
Verify that y=log(x+sqrt(x^2+a^2))^2 s...

Verify that `y=log(x+sqrt(x^2+a^2))^2` satisfies the differential equation `(a^2+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=0.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

Similar Questions

Explore conceptually related problems

Verify that y=e^(m cos^-1 x) satisfies the differential equation (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0

Solution of the differential equation x((dy)/(dx))^(2)+2sqrt(xy)(dy)/(dx)+y=0 is

Solve the differential equation (x y^2+x)dx+(y x^2+y)dy=0

Show that y=a cos(log x)+b sin(log x) is a solution of the differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0

Solve the differential equation : log((dy)/(dx))=2x-3y

Solve the differential equation : (dy)/(dx)-y/x=2x^2

Solve the differential equation: 2x y \ dx+(x^2+2y^2)dy=0

Solve the following differential equation: x^2dy+(x^2-x y+y^2)dx=0

Verity that y=a/x+b is a solution of the differential equation (d^2y)/(dx^2)+2/x((dy)/(dx))=0.

Solve the differential equation x(d^2y)/dx^2=1 , given that y=1, (dy)/(dx)=0 when x=1

RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Suppose the growth of a population is proportional the umber presen...

    Text Solution

    |

  2. A population grows at the rate of 8% per year. How long does it tak...

    Text Solution

    |

  3. Verify that y=log(x+sqrt(x^2+a^2))^2 satisfies the differential equa...

    Text Solution

    |

  4. Verify that y=c e^(t a n-1x) is a solution of differential equatio...

    Text Solution

    |

  5. Show that the differential equation of which y=2(x^2-1)+c e^-(x^2) is ...

    Text Solution

    |

  6. Form the differential equation corresponding to y^2-2a y+x^2=a^2 by el...

    Text Solution

    |

  7. Show that y=A x+B/x ,x!=0 is a solution of the differential equation x...

    Text Solution

    |

  8. Form the differential equation having y=(sin^(-1) x)^2 +A cos^(-1) x +...

    Text Solution

    |

  9. Show that y=a e^(2x)+b e^(-x) is a solution of the differential equat...

    Text Solution

    |

  10. Show that the function y=(A+B x)e^(3x) is a solution of the equation (...

    Text Solution

    |

  11. Show that y=c x+a/c is a solution of the differential equation y=x(dy)...

    Text Solution

    |

  12. Show that y=acos(logx)+bsin(logx) is a solution of the differential eq...

    Text Solution

    |

  13. Solve the following differential equations: (x^2+y^2)(dy)/(dx)=8x^2-3x...

    Text Solution

    |

  14. Solve the following differential equations: (x^2+3x y+y^2)dx-x^2dy=0

    Text Solution

    |

  15. Solve the differential equation: 2x y \ dx+(x^2+2y^2)dy=0

    Text Solution

    |

  16. Solve the following differential equations: (dy)/(dx)=y/x-sqrt((y^2)/(...

    Text Solution

    |

  17. Solve the following differential equations: [xsqrt(x^2+y^2)-y^2]dx + x...

    Text Solution

    |

  18. Solve the following differential equations: y/x cos(y/x)dx-{x/ysin(y/x...

    Text Solution

    |

  19. Solve the following differential equations: (dy)/(dx)=(x+y)/(x-y)

    Text Solution

    |

  20. Solve the following differential equations: x(dy)/(dx)=x+y

    Text Solution

    |