fractured mixed equations 3 c

**transgalactic** · December 8th 2010, 09:59 AM

$y''+(\frac{x}{1+x})y'+(\frac{1}{1+x})y=0$
for x>-1

i dont know how to solve it
i was told to find a solution by the form of y1=e^x

and getting a solution

how?

**Danny** · December 10th 2010, 03:49 PM

If you multily by $1 + x$ then

$(1+x)y'' + xy' + y = 0$ . Now $\dfrac{d}{dx}(xy'-y) = x y''$ and $\dfrac{d}{dx} (xy) = x y' + y$ .

So, your original equation can be written as

$\dfrac{d}{dx} \left(y' + xy' - y + xy \right) = 0$ .

Your turn!

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