Question

The general solution of the differential equation $100\frac{d^{2}y}{d{x}^2}-20\frac{dy}{dx}+y=0$ is

• A. $y=(c_1+c_{2}x)e^x$
• B. $y=(C_1+c_{2}x)e^{-x}$
• C. $y=(c_1+c_{2}x)e^{\frac{x}{10}}$
• D. $y=c_1{e}^x+c_z{e}^{-x}$

Answer 1

Answer: (C)

Equation in the symbolic form is
$(100D^2-20D+1)y=0$ where $d=\frac{x}{dx}$
$A.E.$ is ${\left(10D-1\right)}^2=0$
$\Rightarrow D=\frac{1}{10}$
$\therefore C.S.$ is $y=\left(C_1+C_{2}x\right)e^{\frac{x}{10}}$