1. ## independant solution question

there is an equation $(p(x)y')'+q(x)y=0$ when p(x) and q(x) are deferentiable
on I.
$y_{1}(x)=u$ $y_{2}=\frac{1}{u(x)}$
y1 and y2 are two independant solutions of a given equation.
show that u(x) makes a first order differential equation

2. you were given the substitution, where are you stuck?

3. $(p(x)u')'+q(x)u=0$

$-(p(x)\frac{1}{u(x)^{2}}u')'+q(x)\frac{1}{u(x)}=0$

i put the solutions i got these two equations
what now?

4. Looks good so far. Why not expand out the derivative in the second equation?