independant solution question

• Nov 13th 2010, 06:43 AM
transgalactic
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
• Nov 13th 2010, 06:55 AM
Krizalid
you were given the substitution, where are you stuck?
• Nov 13th 2010, 07:01 AM
transgalactic
$(p(x)u')'+q(x)u=0$

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

i put the solutions i got these two equations
what now?
• Nov 13th 2010, 10:35 AM
Ackbeet
Looks good so far. Why not expand out the derivative in the second equation?