Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XII  >>  Math  >>  Differential Equations
Answer
Comment
Share
Q)

Given that $\large \frac{dy}{dx} = e^{-2y}$ and $y=0$ when $x=5$. Find the value of $x$ when $y=3$.

$\begin{array}{1 1}(A) \large\frac{e^6-\large9}{\large2} \\ (B) \large\frac{e^4-\large9}{\large2} \\(C) \large\frac{e^6-\large9}{\large3} \\ (D) \large\frac{2e^6-\large9}{\large2}\end{array}$

1 Answer

Comment
A)
Toolbox:
  • Form $\large\frac{dy}{dx}=f(x,y),$ when variables are seperable.
  • we expresss it in the form $f(x)dx=g(y) dy$
  • Then $\int g(y) dy=\int f(x) dx+c$
  • $\int e^{ax} dx=\large\frac{1}{a}$$e^{ax}+c$
Given $ \large\frac{dy}{dx}=e^{-2y}$ and y=0 when x=5
We have to find the value of x when y=3
Let us seperate the variables,
$\Large\frac{dy}{e^{-2y}}$$=dx$
=>$ e^{2y}dy=dx$
On integrating both the sides we get,
$\int e^{2y}dy=\int dx$
=>$\large\frac{1}{2}$$e^{2y}=x+c$
When $y=0$ and $x=5$
$\large\frac{1}{2}$$ e^{2 \times 0}=5+c$
But $e^0=1$
Therefore $\large\frac{1}{2} $$=5+c$
$-c=\large\frac{9}{2}$
When $y=3,$ let us find the value of x
$\large\frac{1}{2} $$e^{2 \times 3}=x+\large\frac{9}{2}$
$=\Large\frac{e^6}{2}-\large\frac{9}{2}=$$x$
$=\Large\frac{e^6-\large9}{\large2}$
Hence the value is $\Large\frac{e^6-\large9}{\large2}$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...