# A challenge for all....

#### susi

Joined Jun 4, 2004
31
isotope_3@hotmail.com

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,
susi

Joined Jan 19, 2004
220
hi
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