Q: solve diff equation:

[2ysin(x)+3y^4*sin(x)cos(x)]dx-[4y^3*cos^2(x)+cos(x)]dy=0

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- Apr 21st 2009, 07:34 PMMathventureplz assist me...
Q: solve diff equation:

[2ysin(x)+3y^4*sin(x)cos(x)]dx-[4y^3*cos^2(x)+cos(x)]dy=0

- Apr 22nd 2009, 04:47 AMJester
- Apr 22nd 2009, 05:21 AMMathventure
- Apr 22nd 2009, 05:52 AMJester
IF your ODE $\displaystyle M dx + N dy = 0$ is not exact ie. $\displaystyle M_y = N_x$ then one looks for an integrating factor $\displaystyle \mu $ such that

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

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

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