# fractured mixed equations 3 c

• December 8th 2010, 09:59 AM
transgalactic
fractured mixed equations 3 c
$y''+(\frac{x}{1+x})y'+(\frac{1}{1+x})y=0$
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?
• December 10th 2010, 03:49 PM
Jester
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

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