Develop the weak form and the finite element model of the following differential equation over an element: − d dx ( a du dx ) + d 2 dx 2 ( b d 2 u dx 2 ) + cu = f for x a < x < x b where a , b , c , and f are known functions of position x. Ensure that the element coefficient matrix K e is symmetric. Discuss the nature (i. e., Lagrange type or Hermite type) of the admissible approximation functions for the development of the finite element model.