Question

$\frac{dy}{dx}=e^{-2y}$ and $y=0$ when $x=5$, the value of $x$ for $y=3$ is

• A. $e^5$
• B. $e^6+1$
• C. $\frac{e^6+9}{2}$
• D. $lo{g}_{e}6$

Answer 1

Answer: (C)

$\frac{e^6+9}{2}$

$\frac{dy}{dx}=e^{-2y}$

$\Rightarrow \int e^{2y}dy=\int dx$

$\Rightarrow \frac{e^{2y}}{2}=x+c$

$\Rightarrow e^{2y}=(x+c)2$

put $(x,y)=(5,0)$

$\frac{1}{2}=5+c$

$c={}^{-9}{/}_2$

for $y=3$

$\Rightarrow e^6=(x-{}^9{/}_2)\times 2$

$e^6=(2x-9)$

$x=\frac{e^6+9}{2}$