Email
Chat with tutor
logo

Ask Questions, Get Answers

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

Solve the differential equation$\Large \frac{dy}{dx}\normalsize =2xy-y$

$\begin{array}{1 1}(A)\;x=c\;e^{\large y-y^2} \\(B)\;y=c\;e^{\large x-x^2} \\ (C)\;c=xy \\(D)\;x\;e^{\large y-y^2}=c \end{array} $

1 Answer

Comment
A)
Toolbox:
  • If $\large\frac{dy}{dx}$$=f(x,y),$ where variables are seperable.
  • We express it in the form $f(x)dx=g(y)dy$
  • Then $\int f(x)dx=\int g(y)dy$
  • $\int \large\frac{dx}{x}$$=\log |x|+c$
Given $\large\frac{dy}{dx}$$=2xy-y$
This can be written as
$\large\frac{dy}{dx}$$=y(2x-1)$
On seperating the variables we get,
$\large\frac{dy}{y}$$=(2x-1)dx$
Integrating on both sides we get,
$\int\large\frac{dy}{y}$$=\int (2x-1)dx$
$\log _e y=\bigg( \large\frac{2x^2}{2}-x\bigg)+c$
=>$\log _e y=x^2-x+c$
Converting this to exporential form we get,
$c\;e^{\large x-x^2}=y$
Hence the required equation is
$y=c\;e^{\large x-x^2}$
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.
...