Consider the differential equation:

dx

2

d

2

u

​

+u=x

2

for 0<x<1 under two sets of boundary conditions: Set 1:u(0)=0,u(1)=0 Set 2: u(0)=0,

dx

du

​

∣

∣

​

x=1

​

=1 Determine and numerically evaluate the three-parameter Ritz solutions (i.e., n=3 ) using algebraic polynomial approximation functions for both sets of boundary conditions. Plot and compare the results with the analytical solutions. (Hint: The analytical solution for Set 1 boundary condition is u(x)=

sin1

sinx+2sin(1−x)

​

+x

2

−2. The analytical solution for Set 2 boundary condition is u(x)=

cos1

2cos(1−x)−sinx

​

+x

2

−2.)

I want complete solution of set 2 only