Question

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

• A. $ y = (c_1 + c_2x)e^x$
• B. $ y = (C_1 + c_2x)e^{-x}$
• C. $y = (c_1 + c_2x)e^{\frac{x}{10}}$
• D. $y = c_1e^x + c_ze^{-x}$

Answer 1

Answer: (C)

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