a. use dsolve command in matlab to find an explicit solution of the above BVP. let w(x) = 24EI and L=1(so we are applying a constant load to the beam of length 1)

b.using matlab, plot your solution from part a) over 0?x?1

3. The following BVP models the deflection of a beam that is embedded at both ends (for example, a beam between two walls) dty dx4 E1_=w(x), y(0)=0, y'(0)=0, y(L)-0, y, (L)=0, where . E is Young's modulus of elasticity of the material of the beam, . I is the moment of inertia of a cross section of the beam, . L is the length of the beam, . x is a point along the beam, w(x) is the load per unit length that is being applied to the beam, and . y(x) is the deflection of the beam from its original position. Note that the downward direction is positive. So, for example, if the beam is deflected 2 units below its original position at the point x, then y(x) 2 3. The following BVP models the deflection of a beam that is embedded at both ends (for example, a beam between two walls) dty dx4 E1_=w(x), y(0)=0, y'(0)=0, y(L)-0, y, (L)=0, where . E is Young's modulus of elasticity of the material of the beam, . I is the moment of inertia of a cross section of the beam, . L is the length of the beam, . x is a point along the beam, w(x) is the load per unit length that is being applied to the beam, and . y(x) is the deflection of the beam from its original position. Note that the downward direction is positive. So, for example, if the beam is deflected 2 units below its original position at the point x, then y(x) 2