Which of the following is a solution of the differential

Direction: The complete solution of the ordinary differential equation

	d²y	+ p	dy	+ qy = 0 is
	dx²		dx

y = c₁e^-x + c²e^-3x

Which of the following is a solution of the differential equation d²y + p dy + (q + 1)y = 0 ?
dx² dx

	d²y	+ p	dy	+ (q + 1)y = 0
	dx²		dx

∴ D² + pD + (q + 1) = 0
⇒ D² + 4D + 4 = 0
Since, p = 4, q = 3, therefore

⇒ D =	-4 ± √16 - 16	= -2
	2

Hence, it's solution is, = xe^Dx = xe^–2x

Which of the following is a solution of the differential equation	d²y	+ p	dy	+ (q + 1)y = 0 ?
	dx²		dx