Given the strong form: $[-$d$/$d x$[(-1-$x$)$ d u$/$d x$]=0,$ for $0<3$; u$(0)=1,$ u$(3)=7]$ obtain the weak form which should look like: B$($u$,$ w$)=$I$($w$)$ Using this weak form, let us seek to find a three$-$parameter approximate solution to this problem the looks like: u$\_$N$=\_0($x$)+$c$\_1\_1($x$)+$c$\_2\_2($x$)+$c$\_3\_3($x$)$ L$.$e$,$ our problem now reduces to finding the best values for c$\_1,$ c$\_2$ and c$\_3.$ Let me provide: $[\_0($x$)=1+2$ x; $\_1($x$)=$x$(3-$x$)$; $\_2($x$)=$x$^2(3-$x$)]$ and $\_3($x$)=$x$^3(3-$x$)$ Solve for c$\_1,$ c$\_2$ and c$\_3$ using the Ritz method $($as discussed in class$).$ I$($u$)=1/2$ B$($u$,$ u$)-$l$($u$)$ In the above, when you replace u by u$\_$N$,$ then I will become a function of c$\_1,$ c$\_2,$ c$\_3.$ Now, solve for c$\_1,$ c$\_2,$ c$\_3$ by minimizing this I, L$.$e$,$ solve minimize$\_$c$\_1,$ c$\_2,$ C$\_3$ I$($c$\_1,$ c$\_2,$ c$\_3)$