The simple beam shown above has moments 2M and M acting at the ends. Derive the equation of the deflection curve, and then determine the maximum deflection. Use the third-order differential equation of the deflection curve (the shear-force equation).
I've found that the differential shear-force equation is EIv'''=-(3M)/L. By integrating both sides I found that the bending moment equation is EIv''=-(3Mx)/L+C1. Using the condition that v''((2L)/3)=0 the equation becomes EIv''=-(3Mx)/L+2M. Finally integrating this equation yeilds EIv'=-(3Mx2)/(2L)+2Mx+C2. At this point I'm stuck, what condition do I need to use in order to solve for the constant of integration C2?