Question

The general solution of the different 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. $y = c_{1}\,e^{x}+c_{2}\,e^{-x}$

Answer 1

Answer: (C)

$y = \left(c_{1} + c_{2} \,x\right)e^{\frac{x}{10}}$

Answer 2

Equation is given by
$100\, p^{2}-20\, p+1=0$
$(10 \,p-1)^{2}=0,\, p=\frac{1}{10}, \,p=\frac{1}{10}$
$\therefore$ General solution is
$y=\left(c_{1}+c_{2} \,x\right) e^{\frac{x}{10}}$