5. Solve the linear, constant coefficient ODE y” – 3y’ + 2y = 0; y(0) =…

5. Solve the linear, constant coefficient ODE y” – 3y’ + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y” – 4xy’ + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE ” + 2y’ – 15y = 3x 8. A 2 kg mass is attached to a spring whose constant is 18 N/m, and the entire system is submerged in a liquid which imparts no damping force. If no other external forces are applied, and the mass is released from rest at a position 50cm below the equilibrium, find the equation of motion of the mass [i.e., set up and solve IVP).