Please help me to solve the following differential equation:
$\displaystyle \frac{d^3y}{dx^3} + y = e^{2x}\cdot sinx +e^{\frac{x}{2}} \cdot sin(\frac{\sqrt 3}{2})x$
Thanks in advance...
This is a standard third-order ODE with constant coefficients. There are multiple ways to solve it. Look here at posts 6, 7, and 14. Any of those would work.
Incidentally, you should be more careful with your parentheses on the last term. Use \sin in LaTeX instead of sin.