subject to boundary conditions u(0) = 0, u'(1) = 0

in terms of u(x) = ...

i get u(x) = sin(pi*x) - pi*x , but i think its very wrong

any help much appreiciated thanks !

Not quite right. Certainly that u satisfies the differential equation and u(0)= 0- pi(0)= 0. But u'= pi cos(pi x)- pi so u'(1)= pi cos(pi)- pi and, since cos(pi)= -1, u'(1)= -pi- pi= -2pi, not 0. But that's easy to fix!