Q. The general solution of the differential equation $100\ \frac{d^{2}y}{dx^{2}} - 20\ \frac{dy}{dx} + y = 0$ is
A) $y = \left( c_{1} + c_{2}x \right)e^{x}$
B) $y = \left( c_{1} + c_{2}x \right)e^{- x}$
C) $y = \left( c_{1} + c_{2}x \right)e^{\frac{x}{10}}$
D) $y = c_{1}e^{x} + c_{2}e^{- x}$
Explanation
(c)
Differential equation is
$100\ \frac{d^{2}y}{dx^{2}} - 20\ \frac{dy}{dx} + y = 0$
Here Auxiliary equation is
$\left( 100m^{2} - 20m + 1 \right)y = 0$
$\Rightarrow$ $(10m - 1)^{2}y = 0$
$\Rightarrow$ $m = \frac{1}{10},\frac{1}{10}$
Hence the required solution is
$y = \left( c_{1} + c_{2}x \right)e^{\frac{1}{10}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.