Homogeneous Function - Application To Differential Equations

Application To Differential Equations

The substitution v = y/x converts the ordinary differential equation

where I and J are homogeneous functions of the same degree, into the separable differential equation

Read more about this topic:  Homogeneous Function

Famous quotes containing the words application to, application and/or differential:

    “Five o’clock tea” is a phrase our “rude forefathers,” even of the last generation, would scarcely have understood, so completely is it a thing of to-day; and yet, so rapid is the March of the Mind, it has already risen into a national institution, and rivals, in its universal application to all ranks and ages, and as a specific for “all the ills that flesh is heir to,” the glorious Magna Charta.
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    I conceive that the leading characteristic of the nineteenth century has been the rapid growth of the scientific spirit, the consequent application of scientific methods of investigation to all the problems with which the human mind is occupied, and the correlative rejection of traditional beliefs which have proved their incompetence to bear such investigation.
    Thomas Henry Huxley (1825–95)

    But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.
    Antonin Artaud (1896–1948)