logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

General solution of differential equation: $\large\frac{dy}{dx}$$=xe^{y-x^2}$

$(a)\;e^{-y^2}=2e^{-x} +c \\ (b)\;e^{-y}=2e^{-x^2} +c \\ (c)\;2e^{-y^2}=e^{-x^2} +c \\ (d)\;2e^{-y}=e^{-x^2} +c $
Can you answer this question?
 
 

1 Answer

0 votes
$\large\frac{dy}{dx}=\frac {xe^y}{e^{x^2}}$
$e^{-y} dy=xe^{-x^2}dx$
$\int e^{-y} = xe^{-x^2}dx$
$-x^2=t \qquad -2xdx=dt$
$+e^{-y}=+ \int e^t \large\frac{dt}{2}$$+c$
$e^{-y}=\large\frac{1}{2}e^t +c$
$2e^{-y}= e^{-x^2} +c$
Hence d is the correct answer.
answered Feb 4, 2014 by meena.p
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...