Question

If $y^{\prime \prime }-3y^{\prime }+2y=0$ where $y(0)=1$, $y^{\prime }(0)=0$, then the value of $y$ at $x=lo{g}_{e}2$ is

• A. 1
• B. -1
• C. 2
• D. 0

Answer 1

Answer: (D)

$\frac{d^{2}y}{d{x}^2}-3\frac{dy}{dx}+2y=0$
The corresponding equation is $m^2-3m+2=0$
$\therefore$ General solution of given equation
$y=A{e}^x+B{e}^{2x}$
$y^{{}^{\prime }}=A{e}^x+2B{e}^{2x}$
At $x=0,y=1$
$\Rightarrow A+B=1$
and $x=0,y^{{}^{\prime }}=0$
$\Rightarrow A+2B=0$
Solving these equation $A=2,B=1$
$\therefore y=2e^x-e^{2x}$
At $x=\log 2,y=0$