Solving differential equations with given initial conditions

Question

Differential Equations

Q1. Solve the differential equation with the given initial conditions:

 d²x / dt² + dx/dt + x = 0, t = 0; x = 4/3 ; dx/dt = 3 - √3/ 3

Q2. Solve the differential equation with the given initial conditions:

d²x / dt² + 2dx /dt + x = 0, t= 0 ; x  = -4; dx /dt = -3

Provide complete and step by step solution for the question and show calculations and use formulas.