How to solve the following differential equation?
Favorites|Homepage
Subscriptions | sitemap
HOME > > How to solve the following differential equation?

How to solve the following differential equation?

[From: ] [author: ] [Date: 14-04-10] [Hit: ]
......
dy/dx= e^(2x+y)

obtaining an expression for y in terms of x
where y=0 when x=0

-
dy/dx = e^(2x + y)
dy/dx = e^(2x) * e^(y)
dy / e^(y) = e^(2x) * dx
e^(-y) * dy = e^(2x) * dx

Integrate

-e^(-y) = (1/2) * e^(2x) + C

y = 0 when x = 0

-e^(0) = (1/2) * e^(0) + C
-1 = (1/2) * 1 + C
-3/2 = C

-e^(-y) = (1/2) * (e^(2x) - 3)
e^(-y) = (1/2) * (3 - e^(2x))
-y = ln((3 - e^(2x)) / 2)
y = ln(2 / (3 - e^(2x)))
1
keywords: solve,to,the,How,equation,differential,following,How to solve the following differential equation?
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .