A challenge for all....

Discussion in 'Math' started by susi, Jun 6, 2004.

  1. susi

    Thread Starter Active Member

    Jun 4, 2004

    hi freindzz,

    m having a gr8 trouble in solving these questions..actually m not dat gud in Integration( I thought i was)...newayz help me in solving or atleast gimme the hint how to solve it..

    Solve the Exact Differential Equations:

    1) ( 1 + lnx + y/x) dx + ( cosx + xcosy)dy = 0

    2) {( 1/x + 1/(x^2 )- y/[(x^2)+(y^2)]}dx + { y(e^2) + x /[( x^2)+(y^2)]}dy = 0

    Can any expert of differential equations solve these difficult questions??...

    I know the methology its:

    1st condition > ∂M/∂y=∂N/∂x
    2nd condition > ∂f/∂x=M , ∂f/∂y=N

    but cant solve these question...It is a challenge for all out there..if u can do it!.
    waiting for a response,
  2. haditya

    Senior Member

    Jan 19, 2004
    i dont think the differential equations are exact
    A exact differential equations is of the form

    M dx+N dy = 0 is exact iff
    1. there exists a function U(x,y) such that Mdx+Ndy= dU
    2. the working condition for an exact differential equation is ∂M/∂y=∂N/∂x
    ie if condition 2 is satisfied then the differentila equation is said to be exact.

    therefore going by this neither differential equation turns out to be exact.

    the general solution to a exact diff equation is given by

    ∫Mdx (taking terms of y as constants)+ ∫(terms of N that are independent of x)dy=c