Problem 1 Using the approximation function: A(x) = 2n + aqx + azxl Determine your best approximation to the solution of the differential equation: dy -7 + 10x3 = 0 dx2 Consider the following boundary conditions: y(0) = 0, y(10) = 0 Use the placement criterion or least squares. Problem 2 Create a finite element for the solution of the differential equation of problem 1 using the approximation function: A(x) = 20 + a1x Solve the differential equation by assembling 3 elements. As a result of each problem you must present an approach, algebraic development of the problem, Matlab codes and graphs of results.

problem 1 Using the approximation function:

Determine its best approximation to the solution of the differential equation:

Consider the following boundary conditions:

Use the collocation criterion or least squares.

problem 2 It poses a finite element for the solution of the differential equation of problem 1 using the approximation function:

Solve the differential equation by assembling 3 elements.

As a result of each problem you must present an approach, algebraic development of the problem, Matlab codes and graphs of results.