Verify that y$\_(1)$ and y$\_(2)$ are solutions of the given differential equation but that y$=$c$\_(1)$y$\_(1)+$c$\_(2)$y$\_(2)$ is$,$ in general, not a solution.

$,$yy$^(\text{'}\text{'})=(1)/(2)($y$^(\text{'}))^(2)$;$,$y$\_(1)=5,$y$\_(2)=$x$^(2)$

y$\_(1)$y$\_(1)^(\text{'}\text{'})=,=(1)/(2)($y$\_(1)^(\text{'}))^(2)$

y$\_(2)$y$\_(2)^(\text{'}\text{'})=,=(1)/(2)($y$\_(2)^(\text{'}))^(2)$

Now let y$=$c$\_(1)$y$\_(1)+$c$\_(2)$y$\_(2).$ Then we have the following.

yy$^(\text{'}\text{'})=$

$(1)/(2)($y$^(\text{'}))^(2)=$

yy$^(\text{'}\text{'})!=(1)/(2)($y$^(\text{'}))^(2)$