# plz assist me...

• April 21st 2009, 07:34 PM
Mathventure
plz assist me...
Q: solve diff equation:
[2ysin(x)+3y^4*sin(x)cos(x)]dx-[4y^3*cos^2(x)+cos(x)]dy=0
• April 22nd 2009, 04:47 AM
Jester
Quote:

Originally Posted by Mathventure
Q: solve diff equation:
[2ysin(x)+3y^4*sin(x)cos(x)]dx-[4y^3*cos^2(x)+cos(x)]dy=0

If you multiply by $\cos x$ the equation becomes exact.
• April 22nd 2009, 05:21 AM
Mathventure
Quote:

Originally Posted by danny arrigo
If you multiply by $\cos x$ the equation becomes exact.

but what is method to calculate integrating factor cos(x)??
• April 22nd 2009, 05:52 AM
Jester
Quote:

Originally Posted by Mathventure
but what is method to calculate integrating factor cos(x)??

IF your ODE $M dx + N dy = 0$ is not exact ie. $M_y = N_x$ then one looks for an integrating factor $\mu$ such that

$\left(\mu M\right)_y = \left( \mu N \right)_x$

If $\mu = \mu(x)$ only then

$\frac{\mu_x}{\mu} = \frac{M_y-N_x}{N}$ which in your case it is (very fortunate)!