What is the particular solution to this differential equatio

What is the particular solution to this differential equation whose general solution is: y=C₁e^-2x+C₂e^-2x+sin(x) ; where y(0)=1 and y\'(0)=0.

Solution

The general solution to differential equation is given by y=C.F. +P.I.=y_c + y_p,where y_c=C.F. is the complementary function containing arbitrary constants like C₁, C₂ etc.

The complementary function is y_c= C₁e^-2x+C₂e^-2x

The particular solution is y_p = sinx