another differential equation: x dr/dx + r = xsinx

[Clifford]

x dr/dx + r = xsinx

dr/dx + 1/x * r = sinx

I(x)=e^integral 1/x dx = e^lnx = x
d/dx (xr) = sinx
xr = -cosx + c
r = (-cosx + c)/x

the answer to this one is suppose to be: r = (sinx-xcosx+c)/x

I am guessing that I got the wrong integrating factor, but everything seem to work out okay?

 

[galactus]

Re: another differential equation

You forgot to multiply the right side of the equals by x.

\(\displaystyle \int{xsin(x)}dx=sin(x)-xcos(x)+C\)

 

[Clifford]

silly me!

 

[galactus]

Hey Clifford, since these are DE's, you may want to consider putting them in the DE section instead of calculus.

Is it safe to assume you are covering the small DE section normally covered in a Calc II class?.