dy/dx = (cos x)e^(y+sinx)

i mean i put the y's and x's on the same side but couldn't proceed from it. guidance?

- Mar 29th 2010, 03:54 PM-DQ-solve the differential equation by separation of variables dy/dx = (cos x)e^(y+sinx)
dy/dx = (cos x)e^(y+sinx)

i mean i put the y's and x's on the same side but couldn't proceed from it. guidance? - Mar 29th 2010, 04:14 PMKrizalid
$\displaystyle e^{y+\sin x}=e^{y}e^{\sin x}.$

- Mar 29th 2010, 05:32 PMProve It
$\displaystyle \frac{dy}{dx} = \cos{(x)}e^{y + \sin{(x)}}$

$\displaystyle \frac{dy}{dx} = \cos{(x)}e^{\sin{(x)}}e^{y}$

$\displaystyle e^{-y}\,\frac{dy}{dx} = \cos{(x)}e^{\sin{(x)}}$

$\displaystyle \int{e^{-y}\,\frac{dy}{dx}\,dx} = \int{\cos{(x)}e^{\sin{(x)}}\,dx}$

$\displaystyle \int{e^{-y}\,dy} = \int{e^u\,du}$ upon making the substitution $\displaystyle u = \sin{(x)}$. - Mar 29th 2010, 05:49 PM-DQ-
- Mar 29th 2010, 05:55 PMProve It