Differential Equations

Step 1: Write the given differential equation.
The equation is:

Step 2: Find the auxiliary equation.
The auxiliary equation is:

Step 3: General solution.
The general solution of the differential equation is:

Step 4: Check each option.
- (A) : Clearly a solution, since it fits the general solution.
- (B) : Also a solution, since it fits the general solution.
- (C) : Not a solution, because the constant term does not satisfy the equation.
- (D) : Not a solution, because the constant term does not satisfy the equation.

Step 5: Conclusion.
Thus, the correct solutions are (A) and (B), making the correct answer (2) A and B only.