Q. The order of differential equation whose general solution is given by $y = c_{1}e^{2x + c_{2}} + c_{3}e^{x} + c_{4}\sin{(x + c_{5})}$ is
A) 5
B) 4
C) 3
D) 2
Explanation
(b)
Given equation is
$y = c_{1}e^{2x + c_{2}} + c_{3}e^{x} + c_{4}\sin{(x + c_{5})}$
$= c_{1}e^{c_{2}}e^{2x} + c_{3}e^{x} + c_{4}(\sin{x\cos{c_{5} + \cos{x\sin{c_{5})}}}}$
$= Ae^{2x} + c_{3}e^{x} + B\sin{x + D\cos x}$
Here, $A = c_{1}e^{c_{2}},\ B = c_{4}\cos{c_{5},\ D = c_{4}\sin c_{5}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.